Practice. 1. Circle the rational numbers: Answer: all are rational except Evaluate 6 2(9 2( 1 + 3)) Answer: 4

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1 - Practice These sample problems are a fair, but not comprehensive or verbatim, representation of what to expect on the test. Also study your class notes and homework. You should be able to work these without the aid of calculators or notes. Practice. Circle the rational numbers: Answer: all are rational except. Evaluate 6 (9 ( + 3)) Answer: 4 3. Suppose x + 3 < 7. (a) The distance between x and is less than. Answer: -3, 7 (b) Sketch this set on the number line. (c) Write this set in interval notation. Answer: ( 0, 4) (d) Write this set as a regular inequality. Answer: 0 < x < 4 (e) Is the set open or closed? Answer: open 4. Use a single absolute value inequality to describe the set (, ] [9, ). Answer: x Solve the equation: (a) (x 7) = 6 5x Answer: x = 0 7 (b) x = 4 Answer: x = ± (c) (3x ) = Answer: 3x = ±, so x = 4, 0 3 (d) x + = 7 Answer: x = 6, 8 (e) x + = 7 Answer: x + = ±7, so x = 6, 8 and x = 3, 4 (f) x+ = 3 x Answer: x = 3 (g) x(5x 4)(x + 3) = 0 Answer: x = 0, 4/5 6. Circle the solution(s) to the equation: x + 8 = x 4. (a) -7 (b) -4 (c) (d) 4 (e) 8 Answer: plug in to see that x = 8 is the only solution 7. Multiply out and simplify completely by collecting like terms: x(x + 7) + 3(x 4) Answer: x 38x Circle the letters corresponding to true statements.

2 - Practice (a) x describes the interval (, ] [, ) (b) x y y x = (c) (x )( + x) = x x (d) a + b = a + b (e) 3 = ( 3) (f) (x + h) = x + h (g) ( x) = x (h) x + = x+ 9. Solve the inequality 3x 7 5, and write your solution in interval notation. Answer: This is a restraining order, so expect two parts to the solution set. If 3x 7 5, then we get 3x and x 4. If 3x 7 5, then we get 3x and x /3. The solution is (, /3] [4, ). 0. Evaluate the following. (a) Answer: (b) 9 3 Answer: 7 (c) 4 5 Answer: 00 (d) ( ) 3 0 Answer: 0. Simplify the following by removing radicals and combining exponents. ( y 4 x 5 8x / y ) /3 Answer: x y. Find the arithmetic and geometric means of these numbers: {,,, 8} Answer: arithmetic: 4 = 3; geometric: 6/4 = 3. The human life expectancy is.4 billion seconds. Write this number in scientific notation. Answer: In twelve years, Bubba will be 80 percent older than he was four years ago. (a) Write an algebraic equation for this problem. Answer: Let x be Bubba s current age. Then x + =.8(x 4). (b) How old is Bubba now? Answer: x + = 9 5 (x 4), multiply thru by 5 to get 5x + 60 = 9x 36 or 4x = 96 and x = 4 5. In the SAC basketball tournament, Andy scored 5 points in the first game and 7 points in the second game. (a) If he scores x points in the third game, write an expression for his scoring average. Answer: 4+x 3 (b) How many points must he score in the third game in order to average 30 points per game in the tournament? Answer: x = Suppose you leave Knoxville at :00, and need to be in Roanoke, VA by 4:00. This is a 60 mile trip. If it takes you :30 to go the first 00 miles, how fast must you drive the rest of the way to get there on time? Answer: You have.5 hours remaining to drive 60 miles, so you must average 60.5 = 64 MPH. 7. Find the distance between: (a) and -7 Answer: 7 = 9

3 3 - Practice (b) P(, 5) and Q( 4, 3) Answer: = 0 (c) P and R, where R is the midpoint of PQ. Answer: 0 = 5 8. Find the point that is one-quarter of the way from ( 3, 5) to (9, ). Answer: do the midpoint twice to get (0, 4) 9. Consider the line 3y x = (a) Find the x-intercept. Answer: x = 6 (b) Find the y-intercept. Answer: y = 4 (c) Find the slope. Answer: m = /3 0. Find the equation of the line that goes through (4, 3) and (9, ). Answer: the slope is m = = /5, so the eqn of the line is y = (x 4). Find the equation of the line that has x-intercept, and also goes through (, 6). Answer: the points are (, 0) and (, 6), so the slope is m =, and the eqn is y = 6 (x + ). Suppose that a 5 year old boy weighs 43 pounds, and that every year after that he gains pounds. (a) Write the equation of a line that describes this child s weight. Let x be his age, and y his weight. Answer: y = 43 + (x 5) (b) When will he weigh 75 pounds? Answer: solve 75 = 43 + (x 5) to get x = 6 3. Circle the letters corresponding to true statements. (a) Any triangle that satisfies the Pythagorean Theorem must be a right triangle. (b) P(, ) is in the third quadrant. (c) The slope of 3x + 9 = y is m = 6 (d) 9 = 9 (e) If a line s x and y intercepts are both negative, then the slope is positive. (f) (5, 5) is farther from the origin than (7, ) 4. Find the equation of the line that goes through (, 5) parallel to 3x 8y = 0. Answer: Since y = 0 3x 8, the desired slope is m = 3 8, so the eqn of the parallel line is y = (x ). 5. Dwight Schrute receives a base salary of $30 thousand dollars. In addition, for each client he signs beyond the first four, he receives a $ thousand bonus. (a) If he signs 7 clients, what is his total income? Answer: 30 + (7 4) = 36 (b) Write a general formula if he signs x clients. Answer: y = 30 + (x 4) (c) If he made $44 thousand, how many clients did he sign? Answer: solve 44 = 30 + (x 4) to get x = 6. A European tourist arrived in New York and exchanged 700 Euros for 000 dollars. Returning home, she had 50 dollars left over, which she converted back into Euros. 700 Answer: 000 = x 50, so x = 35

4 4 - Practice 7. Given two points P(4, 3) and Q(, ), find the equation of the line that intersects the midpoint of PQ at a right angle. Answer: The slope of PQ is 4/3, so to be perpendicular we want m = 3/4. The midpoint is (, 7) so the eqn of the line is y = (x ). 8. Suppose the number of women that Casanova dates in a month is proportional to the number of pickup lines that he uses. Last month he used 63 pickup lines and went on 4 dates. This month he used 45 pickup lines. How many dates did he get? Answer: Let y be the dates and x the pickup lines, so that y = mx. Solving 4 = m 63 gives a slope of m = /9. So when x = 45 we get y = Brutus and Popeye went out to dinner. Brutus ordered 4 steaks and one side of spinach for $3. Popeye ordered steaks and 7 sides of spinach for $9. (a) Write two linear equations describing this situation. Answer: 4S + P = 3 and S + 7P = 9 (b) A steak costs and spinach costs. Answer: use substitution to get S = 7.5 and P = 30. Where do these lines intersect? 3x = 5y + x 3y = 8 Answer: use substitution; they intersect at (7, ) 3. Santa s elves can make 5 dolls and 3 trains in 8 minutes. They can make dolls and 7 trains in 73 minutes. (a) Write a system of linear equations describing this situation. Answer: 5D + 3T = 8 and D + 7T = 73 (b) Use substitution to solve the equations. It takes minutes to make a doll, and minutes to make a train. Answer: and 7 3. Circle the letters corresponding to true statements. (a) x = 4 is a vertical line (b) The lines y = 3x and 3y + x = 4 are parallel. (c) The perimeter of a square is proportional to the length of a side. (d) The viewing area of a TV screen is proportional to the length of its diagonal. 33. Circle the letters corresponding to true statements. (a) A function could have two y-intercepts. (b) This is a function: {(, ), (, ), (3, )} (c) f(x) = (x 3) goes through (, ) (d) If W = 3t t, then t is the dependent variable. (e) 5y x = 7 is a linear function. (f) If f(x) = x then f(x) = x., it is (x) = 4x 34. Find the center, radius, area, and circumference of this circle: 9 y = (x ). Answer: (, 0), r = 3, A = 9π and C = 6π 35. Which of these formulas describe circles? If it is a circle, identify the center and radius.

5 5 - Practice (a) x = 9 (y + ) Answer: circle; (0, ), r = 3 (b) (x + ) + (y 3) = 0 Answer: not circle (c) (x 3) 3 = y Answer: circle; (3, 0), r = 5 (d) (x + 3) (y 9) = 4 Answer: not circle 36. Find the equation of the circle that is centered at (, 7) and has a y-intercept at 4. Answer: since it goes thru (0, 4) we find that r = ( 0) + (7 4) = 3, and thus the eqn of the circle is (x ) + (y 7) = Belinda Carlisle s pop 80 s hit Circle in the Sand was referring to a circle with diameter that stretches from P(3, 0) to Q(, 6). Find the equation of this circle. Answer: use the midpt formula to get the center (, 3), and use the distance formula to get r = 3, so the eqn is (x ) + (y 3) = 3 ( An astronaut in orbit h miles above the Earth weighs W = h) pounds. (a) is the independent variable, and is the dependent variable. Answer: h is indep, and W is dep (b) How much does he weigh on Earth? Answer: If h = 0 then W = 80. (c) Suppose that the astronaut s weight is 0 pounds. How many miles high is he? Answer: If W = 0 then h = 8000 miles. 39. Let f(x) = 3(x + )(4x )(x 9) (a) Find the y-intercept. Answer: f(0) = 7 (b) Find the x-intercept(s). Answer: set f(x) = 0 to get x =, /4, ±3 40. Find the equation of the line that connects the x and y intercepts of f(x) = x +. Answer: The y-int is (0, ) and the x-int is (3, 0). The slope between these points is m = 3, and the equation of the line is y = + 3 (x 0). 4. If the point ( 3, y) is on the unit circle in the third quadrant, what is y? Answer: The unit circle is described by the equation x + y =. Solve ( /3) + y = to get y = 8/9, so y = ± 8 3. We want the point to be in the 3rd quadrant, so pick the negative answer y = 8/3. 4. Brittany has a cell phone plan that charges $30 per month, plus 0 cents for every minute over a 500 minute limit. Let x be the number of minutes, and f(x) the total charge. (a) Assuming she talks for at least 500 minutes, write a formula for f(x) Answer: f(x) = 30 +.(x 500) (b) If she talked for 950 minutes, what was her bill? Answer: f(950) = 75 (c) If her bill comes to $50, how many minutes did she talk that month? Answer: set f(x) = 50 and solve for x = Plot several points and sketch the graph of f(x) = x 4. Answer: connect the dots for the points {( 3, 5), (, 0), (, 3), (0, 4), (, 3), (, 0), (3, 5)} 44. If your fixed cost is $00, and you can make CN professor bobble-heads for $5 each and sell them for $8 each, write your profit as a function of units sold, x. Answer: total cost is C = 00+5x, and revenue is R = 8x. Therefore profit is P = 8x (00 + 5x) 45. If f(x) = x + 3x, compute and simplify f(x) f(x). Answer: (x + 3x) ((x) + 3(x)) = x + 6x 4x 6x = x

6 6 - Practice 46. Write the formula for a function that would have this graph x 4 5 Answer: shifted right, up, flipped, and scaled by, so y = x Sketch the graph of: (a) f(t) = t 3 Answer: same as y = x 3 (b) y = (x + 3) / Answer: shift x left 3 (c) f(x) = x Answer: /x flipped t +t (d) V = Answer: plot points 48. Given the graph of f(x), the graph of f(x + 4) has the same shape but shifted: (a) right up 4 (b) left up 4 (c) left 4 down (d) right 4 down (e) down right 4 Answer: left 4, down 49. Is the function f(x) = x +x even, odd, or neither? What does that say about graph s symmetry? Answer: f( x) = x +x = f(x), so the function is odd, which means it is symmetric with respect to the origin. 50. Circle the letters corresponding to true statements. (a) If f( x) = f(x) then the graph is symmetric about the origin., it is even, not odd (b) y = 3x is a fat parabola. (c) f(x ) has the graph of f(x) shifted left (d) f(x) = x is an odd function. 5. Let f(x) = 6 x + (a) Find the y-intercept. Answer: f(0) = 4 (b) Find the x-intercept(s). Answer: solve 0 = 6 x + to get x + = 3, so x =, 4 (c) What is the domain of f? Answer: R (d) What is the range of f? Answer: sketch the graph to see that the V shape opens down from (, 6), so the range is (, 6] 5. Find the domain: (a) f(x) = 3x + 5 Answer: we need 3x + 5 0, so x 5 5 3, or equivalently [ 3, ) (b) f(x) = ( x + ) Answer: write this as y = ( x+ ), so we need x + 0 or x +, so x, 3

7 7 - Practice (c) f(x) = 3 x + Answer: cube roots are always OK, so the domain isr 53. Find the range: (a) y = x+ 3 Answer: [0, ) (b) y = 4 x Answer: (, 4] (c) The top half of the unit circle. Answer: [0, ] (d) f(x) = (x 3) Answer: x 3 moved around always has ranger (e) y = (x 3) + 7 Answer: x moved right 3, up 7, so the range is [7, ) (f) f(x) = x Answer: Plot points to see that there is a horizontal asymptote at y = 0, but y is always positive. The range is (0, ). 54. If f(x) = x x+3, find the equation of the secant line between points where x = and x = 6. Answer: the two points are (, ) and (6, ), so the slope is m = 4 8, and the equation of the secant line is y = + (x + ) 55. Find the equation of the secant line that connects the x and y intercepts of f(x) = (x 3)(x + 4). Answer: To get the y-int, set x = 0 to get (0, ). To get the x-int, set y = 0 to get (3, 0). The slope is m = = 4. Using the point (3, 0) the eqn of the line is 56. At which labeled point(s) is the graph y = 0 + 4(x 3) B E F A C D (a) increasing Answer: A (b) decreasing Answer: C,F (c) concave up Answer: D,F (d) concave down Answer: A,B,E (e) inflection point Answer: C (f) local max Answer: B,E (g) local min Answer: D (h) global min Answer: none (i) global max Answer: E Also, sketch the tangent line to the graph at point B. 57. This table lists the total number of Facebook friends that Gertrude had over the last few months: month friends

8 8 - Practice (a) What was the average rate of change (in friends per month) between months 7 and? Answer: = 6 FPM (b) Write a formula for this secant line. Answer: y = (x ) (c) At this linear rate, predict how many friends she ll have by month 4. Answer: (4 ) = If h(t) = 00 6t is the height (in feet) of an object in free fall, find the average velocity (AROC) between time t = and t = 3. Answer: The two points are (, 84) and (3, 56), so m = = 64 feet per second. 59. Describe in your own words the difference between average and instantaneous rates of change. Use a car s speed to illustrate. 60. Let f(x) = 3x (x 5)(x + 4) 3 (a) What is the degree of f? Answer: 9 (b) Find the roots Answer: x = 0, 5 6. If p(x) = x and q(x) = x + 3, find and simplify: (a) p + q Answer: (x ) + (x + 3) = x + x + (b) p q Answer: (x ) (x + 3) = x 4x 7 (c) pq Answer: (x )(x + 3) = x 3 + 3x x 3 (d) (p + )q Answer: ((x ) + )(x + 3) = x (x + 3) = x 3 + 3x (e) p(x + ) Answer: (x + ) = (x + x + ) = x + x 6. Circle the letters corresponding to true statements. (a) The domain of y = x + isr (b) y = 3 ( x) is concave down. (c) It is possible for a graph to have neither a global minimum nor a global maximum., e.g. f(x) = x (d) Every global max is a local max. (e) The degree of p(x) = (x+3) 5 ( x ) is five. (f) f(x) = x + x + x is a polynomial. (g) x = is a root of p(x) = x 3 5x +. (h) f(x) = (x + ) + has no real roots. (i) Every polynomial has a real root. 63. Factor y = x 3 4x 36x and list the roots. Answer: y = x(x 9)(x + ), so the roots are 0, 9, 64. Find the domain of f(x) = (9x x 3 ). Answer: rewrite this as f(x) = x(3 x)(3+x), so the domain is x 0, 3, Find the range of f(x) = x 4x +. Answer: the vertex is at (, 3), and the parabola opens up, so the range is [ 3, ) 66. Write y = x + x + 7 in standard form by completing the square. Then find the vertex. Answer: y = (x + 3) ; the vertex is at ( 3, ) 67. Find the roots of

9 9 - Practice (a) p(x) = 3(x ) +. Answer: (x ) = 4 so x = 3, (b) y = x 4x 5 Answer: y = (6x 5)(x + ) so x = 5/6, / 68. Find the vertex of (a) y = 3 5 (x + )(x 9) Answer: the vertex is half-way between the roots +9 = 4, plug in to get y, so the vertex is (4, 5) (b) y = 3 5(7 x) Answer: (7, 3) 69. Solve the equation (list all solutions): (a) x + 6x = 3 Answer: use QF to get 3 ± (b) t = (5t + ) Answer: (t )(t + ) = 0 so t =, (c) x 3 + x = 4x + 8 Answer: x (x + ) 4(x + ) = 0 so (x + ) (x ) = 0 and x = ± (d) (3 x) = x x+ Answer: x+ = 3x x so x x+ = 0 and x = 70. Write the quadratic that satisfies the given properties: (a) vertex (, ), passes through (3, ) Answer: (x ) (b) passes through (, 0), (3, 0), and (0, 6) Answer: (x + )(x 3) (c) roots at x = 3 and x =, and goes thru (, 6). Answer: 3 (x + 3)(x ) 7. Consider the quadratic p(x) = 4 (x + ) (a) Write p(x) in general form. Answer: x x + 3 (b) Write p(x) in factored form. Answer: (x + 3)(x ) (c) Find the vertex. Answer: (, 4) (d) Find the roots. Answer: 3, (e) Find the y-intercept. Answer: (0, 3) (f) Find the domain Answer: R (g) Find the range Answer: (, 4] 7. Circle the letters corresponding to true statements. (a) y = 3x x + 4 has its maximum value when x =. (b) (x + ) = x has no real solutions. (c) The maximum of x 4x occurs at x =. (d) The vertex of f(x) = x(x ) is at (0, ). (e) The parabola p(x) = ( x) is concave up. 73. Which of these is closest to a root of y = x 7x + 4 (a) 0 (b) (c) 3 4 (d) (e) 7 Answer: The exact roots are x = 7± 49 3 so the answer is (c) 4 = 7± 7 4. Since 7 4, we obtain x 7±4 4 = /4, 3/4,

10 0 - Practice 74. If cost is P and demand is 75 0P, what price P should you charge to maximize profits? Answer: Y = R C = PD C = 75P 0P 00 5P = 0(P 7P + 0) has a vertex when P = b a = Let f(x) = 8x x. (a) Find the domain Answer: R (b) Find the range Answer: (, 6] (c) Is this function even/odd/neither? Answer: neither 76. Suppose that at price P, the demand for Cogswell Cogs is D = 30(P + ). The supply equation is S = 5(P 4). What is the free-market equilibrium price? Answer: Set S = D to get 5(P 4) = 30 P+, so 5(P 4)(P + ) = 30, so (P 4)(P + ) = 6, so P 3P 0 = 0, so (P 5)(P + ) = 0, so P = 5,. Only the positive answer makes sence, so the equilibrium price is P = Old MacDonald needs to build a fenced in chicken pen next to his barn. He has 60 feet of fence. One side of the rectangular pen is the barn, so the fence only needs to enclose the other three sides. (a) Draw a picture and label the pen s width (w) and length (l). barn W pen W Answer: L (b) Find the dimensions that will maximize the area enclosed by the pen. Answer: We know that w+l = 60, and A = lw. Substitute to get A = w(60 w) = 60w w. The vertex is at w = b/a = 60/ 4 = 5 feet. Then l = 60 w = 30 feet. Therefore the pen should be 5 30 feet. (c) How many square feet of space will the chickens have? Answer: A = 5 30 = 450 square feet. 78. A military surveillance drone reached its target, flying with a 7 MPH tailwind. On the return trip, it had a 9 MPH headwind. If the round trip took 8 hours, and the target was 0 miles away, what is the airspeed of this aircraft? Answer: Let x be the unknown speed of the drone. With the tailwind, D = 0, S = x + 7, and T = 0 x+7. With the headwind, D = 0, S = x 9, and T = 0 x 9 0 x x 9 = 8. The total time was 8 hours, so 0 x x+7 (x + 7)(x 9) = 8 Cross multiply, collect terms, and factor to get x 3x 33 = (x 33)(x + ) = 0. Therefore x = 33 MPH is the speed of the drone. 79. A soccer ball is kicked so that it reaches a maximum height of 5 meters when it has traveled 0 meters in horizontal distance. The goal is 6 meters away and 3 meters high.

11 - Practice (a) Find the equation for the parabolic path of the soccer ball. Answer: Using the vertex y = a(x 0) + 5. Another point is (0, 0), so 0 = a(0 0) +5 and 0 = 00a + 5 implies a = /0. Therefore y = 0 (x 0) + 5 (b) Unfettered, how far away will the ball land? Answer: The other root occurs when x = 0. (c) Would the ball go over the goal, or into it? Answer: When x = 6, y = 0 (6 0) + 5 = > 3, so the ball is over the goal. 80. Given this circle: x + y = 6y 5 (a) Find the center and radius. Answer: complete the square to get x + (y 3) = 4, so the center is (0, 3) and r = (b) Find an equation for the bottom semi-circle, then sketch it. Answer: y = 3 4 x (c) What is the domain? Answer: [, ] (d) What is the range? Answer: [, 3] 8. Solve the following: (a) x = 6x 5 Answer: x =, 5 (b) x < 6x 5 Answer: (, 5) (c) x 6x 5 Answer: [, 5] (d) x 6x 5 Answer: (, ] [5, ) 8. Write with a common denominator and then simplify completely: x + x 3x x + 3 Answer: x+ x 3 x(x+3) = (x+)(x+3) 3 x(x+3) = x +4x x(x+3) = x+4 x Get a common denominator on the left, then solve the equation: Answer: (+x)( x) x(x ) = 3 gives x = / 84. Find the horizontal asymptote: 6 3x x x + x = 3 x (a) y = 3( x)(5x 7) (x 9) Answer: since deg(n) = deg(d), just take the ratio of leading coefficients: y = 30/ = 5 (b) y = x+5 3x 7x+ Answer: since deg(n) < deg(d), the HA is y = If y = x +5x 3 x 3 +

12 - Practice (a) Find the y-intercept. Answer: plug in x = 0 to get y = 3/ (b) Find the root(s). Answer: set y = 0 to get x + 5x 3 = (x )(x + 3) = 0, so x = /, 3 (c) Find the HA. Answer: since deg(n) < deg(d) the HA is y = If y = x(x+) x 3x 4 (a) Find the HA. Answer: ratio of leading coefficients: y = / = (b) Find the VA. Answer: write y = x(x+) (x+)(x 4), so x = 4 is a VA. 87. Consider the rational function f(x) = x(6 x) x 3x+30. (a) Factor and simplify: Answer: 4x(3 x) (x 3)(x 0) = 4x x 0 (b) Solve the equation f(x) = 6 Answer: 6 = 4x x 0, so x = 8 (c) What is the horizontal asymptote? Answer: HA: y = 4 (d) f(x) has vertical asymptote Answer: VA: x = Jared s weight after t months on the Subway diet was (a) What did Jared weigh at the start? Answer: plug in t = 0 to get W = 300 W =.9(t ) (.t + 6)(.05t + 0) (b) How much did he lose in the first 0 months? Answer: plug in t = 0 (use a calculator) to get W = 46, so he lost about 54 pounds (c) What will his weight level out at? Answer: HA is y = Which rational function would have this graph? x 4 x (a) x (b) +x +x (c) 4 +x (d) x x Answer: Look for properties consistent with the graph. The HA is y = 0, and f(0) = 0 so by process of elimination we select b) 90. While working construction in Alaska, Jen has determined that the local population of grizzly bears is on the rise according to the function: 00t + 63 P = t + 7 (a) What was the population when t = 0? Answer: 9 (b) Determine the long-term bear population. Answer: P = 50

13 3 - Practice (c) Sketch the bear population for t 0. Answer: increases from (0, 9) to the HA of Find the equation of the secant line to y = x+7 x +5 between x = 4 and x =. Answer: Plug in to get the two points ( 4, /7) and (, ). The slope is m = /7 ( 4) = 6/7 6 = 7. The secant line is y = + (x ) 7 9. Circle the letters corresponding to true statements. (a) The rational function f(x) = 6x 3x + has horizontal asymptote y =., the HA is y = 0 (b) x = is a root of p(x) = 3x 7 x 4 + 5x 8x +, when x =, y = 0 (c) If the degree of the numerator is greater than the degree of the denominator, then the rational function has asymptote y = 0., if deg(n) > deg(d) then there is no HA (d) f(x) = (x ) x+ has vertical asymptote y =., the VA is x = 93. If f(x) = 9 x, (a) Find the y-intercept. Answer: (0, ) (b) Evaluate f(.5). Answer: 9 3/ = 3 3 = 7 (c) Find the equation of the secant line that connects the y-intercept with the point on the graph where x =.5. Answer: (0, ) and (.5, 7) are the two points, so m = 6.5 = 5 3 and y = x 94. Solve the equation 4 x = 8 x. Answer: solve x = 3(x ) so x = 3(x ) implies x = 3/4 95. Find an exponential function with the following graph (the VA is y = and it goes thru (, 4) and (0, 0)): 6 y Answer: use the points (0, 0) and (, 4) to get y = 8(.5) t + x Suppose the exponential function: y = 5b t + goes through the point (, 3). Then it also goes through the point (a) ( ) 4, 5 (b) ( ) 4, 5 (c) ( ) 4, 5 9 (d) ( 4, 9 5 ) Answer: (d) since solving for b you get y = 5(/5) t/ +, so when t = 4, y = 9/5 97. A room temperature (70 degrees) Pepsi is placed into the refrigerator (38 degrees). After one hour, the Pepsi has cooled to 50 degrees.

14 4 - Practice (a) Create an exponential model for the temperature of the Pepsi after t hours in the refrigerator. Answer: y = ab t + 38, then 70 = a + 38 so a = 3 and y = 3b t + 38, then 50 = 3b + 38 so b = 3/8 and y = 3(3/8) t + 38 (b) What will be the temperature of the Pepsi after two hours? i. 30 ii. 38 iii iv. 4.5 v Answer: plug in t = to get y = 4.5