x 1 2 i 1 5 2i 11 9x 9 3x 3 1 y 2 3y 4 y 2 1 Poudre School District s College Algebra Course Review
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1 . Perform the indicated operations and simplify the result. Leave the answer in factored form. 9x 9 x a. b. 9x 9 x x. Solve: x 7x x 0. a. x., b. x 0,., x,0,. x.,0,. Find the quotient and the remainder of 8x x 7x divided by x. For #6-8, consider the two points (8, ) and (,). 6. Algebraically determine the equation of the line in the form y mx b. 7. Determine the equation of the line perpendicular to the line you found in #6 that passes through the point (, 7). 8. Determine the equation of the circle with endpoints of a diameter at the given points(8, ) and (,). 9. Find the equation of the line that connects the centers of the two given circles. circle #: x y 6x y 0 circle #: x y x 8y 0 For #0-8, use the given graph of the function f to answer the following questions.. Solve: y y y y y. Which expression below is 7i i written in a bi form? a. i b. i i i 0. Find the domain of f (x).. Find the range of f (x).. List the x-intercept(s).. Identify the y-intercept.. Find f ( ).. Is f positive or negative? 6. State the interval for which f (x)is negative. 7. For what value(s) of x is f (x)? 8. f (x) is increasing on what interval?
2 For #9-, let f x x. 9. Evaluate f (). 0. Find f (x h) f (x) h and simplify.. Let A and C 8, B 6 y 0, 8 7. Find AB+C.. Solve f( x ).. Algebraically determine whether the following function is even, odd, or neither. x hx ( ) x. Given f (x) x x determine the average rate of change from to x. Give answer in simplified factored form.. Graph the following piecewise defined function. x if x g if 0 x x if x 0 For #-8, let f x.. State the parent function to which transformations are applie 6. List the sequence of transformations applied to the parent function. 7. Sketch a graph of f (x) with at least points plotte 8. State the domain and range of f (x). 9. Solve the system. x y z x y z 6 x y z. Find the inverse of the following matrix: 7. For #- assume an 8-cylinder Crown Victoria gives 8 miles per gallon in city driving and miles per gallon in highway driving and a family s 00 mile trip required. gallons of gasoline.. Identify the variables in the situation.. Write a system of equations based on the situation.. Solve the system to find how many whole miles were driven in the city? 6. Use the Corner Point principle to maximize z x y subject to the x 0 following constraints. y 0 a. z. 8 b. z z. 6 z x y 6 9x y 7 0. Solve for x, x 9 8
3 7. Perform each row operation in order, () followed by () followed by (), on the given augmented matrix. For #9-, solutions must show appropriate algebraic methods. Let f (x) x x Find the x-intercept(s). 0. Find the y-intercept.. Find the vertex of f(x). ()R R R ()R R R ()R R R 0 a. 0 0 b Is the vertex of f(x) a maximum or minimum? Explain how you know using complete sentences.. Which of the equations below describes the graph shown? a. f (x) x x b. f (x) x x f (x) x x f (x) x x e. None of the above 8. Find the quadratic function in the form y a(x h) k that has a maximum point at (-, -7) and passes through (7, ) a. y (x ) 7 b. y (x ) 7 y (x 7) y (x ) 7. Sketch the given function using the intercepts and end behavior. f x( x ) x x x For #-8 let f x x. State the domain of f(x) 6. Find the x-intercept(s) and y-intercept of f(x)..
4 7. Find all asymptotes and/or holes. 8. Graph f(x). Be sure to plot at least three points and show all asymptotes. 9. One solution of x x x 0 is. Find the two other solutions. a., b.,,, a. f x x b. f x x f x x f x x 6. Given the graph of f x, identify the graph below that shows the graph of f. (Note the x and y scale is ) For #0- let y x x x x. 0. Determine the left and right hand behavior of the graph of y.. Find all the zeros of the function.. Write the polynomial as a product of linear factors.. Use the given zero to find the all remaining complex zeros of the given function. h( x) x 9 x x 79 x Given: + i is a zero. 78. Find the indicated composite f g x for the pair of functions f x 9 and g 8x. a. x b. 8 x 9 8 x x. Find the inverse function of x f. (choices above) x
5 7. Use the properties of logarithms to find the exact value of the expression log 00 (log 8 log ). a. - b Write log () log ( x ) log as a single logarithm with a coefficient of. 9. If x what does x 8 equal? 60. An initial deposit of $,000 is made in a savings account for which the interest is compounded continuously. The balance will double in seven years. What is the annual rate of interest for this account? a..% b. 6.% 8.% 9.9% 6. Determine how long it takes a $000 investment to double if it is invested at 8% compounded semiannually. a. 9. years b. 9 years 8.8 years 8.6 years x 6. Solve the equation e for x. Round your answers to three decimal places. 6. Solve the equation log( x ) log x for x. Check for extraneous solutions. 6. Write the partial fraction decomposition of the rational expression. x x 8x x ( x )( x ) 6. The half-life of silicon- is 70 years. If a sample presently contains 0 grams, which expression determines how much silicon- material will remain after 60 years? a. 0 e 60k where k ln(0.) 70 ln(0.) b. 0 e 60k where k 60 k ln(0.) 60 e where k 70 ln(0.) 70 e 60k where k 0
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