Solve the problem. Determine the center and radius of the circle. Use the given information about a circle to find its equation.

Transcription

1 Math1314-TestReview2-Spring2016 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) Is the point (-5, -3) on the circle defined by (x + 2) 2 + (y - 1) 2 = 25 1) A) Yes B) No Determine the center and radius of the circle. 2) (x - 2) 2 + (y - 5) 2 = 75 2) A) Center: (2, 5); Radius: 5 3 B) Center: (-2, -5); Radius: 75 C) Center: (-2, -5); Radius: 5 3 D) Center: (2, 5); Radius: 75 Use the given information about a circle to find its equation. 3) center (-7, -9) and diameter 10 3) A) (x + 7) 2 + (y + 9) 2 = 100 B) (x + 7) 2 + (y + 9) 2 = 25 C) (x - 7) 2 + (y - 9) 2 = 25 D) (x - 7) 2 + (y - 9) 2 = 100 1

2 Write the equation in standard form to find the center and radius of the circle. Then sketch the graph. 4) x 2 + y 2 + 4x - 21 = 0 4) A) (x + 2) 2 + y 2 = 25 B) (x + 2) 2 + y 2 = 25 C) (x + 2) 2 + y 2 = 16 D) (x + 2) 2 + y 2 = 16 2

3 For the given relation, write the domain, write the range, and determine if the relation defines y as a function of x. 5) 5) A) Domain: {-4, 1, 4}; Range: {-3, -1, 4}; not a function B) Domain: {-3, -1, 4}; Range: {-4, 1, 4}; not a function C) Domain: {-4, 1, 4}; Range: {-3, -1, 4}; function D) Domain: {-3, -1, 4}; Range: {-4, 1, 4}; function Determine whether the relation defines y as a function of x. 6) 6) A) Not a function B) Function Evaluate the function for the indicated value, then simplify. 7) f (x) = -5x - 5; find f (a - 3), then simplify as much as possible. 7) A) a + 10 B) -5a - 8 C) -5a + 10 D) a ) f (x) = -4x 2-2x; find f (-4) 8) A) -66 B) 264 C) 24 D) -56 3

4 Determine the x- and y-intercepts for the given function. 9) f (x) = x - 8 9) A) x-intercept: (64, 0); y-intercept: (0, -8) B) x-intercept: (-8, 0); y-intercept: (0, 64) C) x-intercept: (-8, 0); y-intercepts: (0, -64) and (0, 64) D) x-intercepts: (-64, 0) and (64, 0); y-intercept: (0, -8) Determine the domain and range of the function. 10) 10) A) Domain: (-, -1]; Range: [-4, ) B) Domain: (-4, ); Range: (-, -1) C) Domain: [-4, ]); Range [-3, - ) D) Domain: [-4, ); Range: (-, -1] Write the domain in interval notation. 11) f(x) = x - 1 x ) A) (-, -8) (-8, ) B) (-, -1) (-1, ) C) (-, 1) (1, ) D) (-, 8) (8, ) 8 12) f(x) = 6 - x A) [6, ) B) (-, 6] C) (-, 6) D) (6, ) 12) Find the slope of the ramp pictured below. 13) 13) A) -88 B) 25 3 C) 88 D)

5 Determine the slope of the line passing through the given points. 1 14) 2, 3 2 and - 3 2, ) A) m = B) m = 20 9 C) m = 9 20 D) m = 9 10 Write the equation in slope-intercept form and determine the slope and y-intercept. 15) -4x = -3y ) A) y = x + 12; slope: - 4 ; y-intercept: (0, 12) 3 B) y = x - 4; slope: - 4 ; y-intercept: (0, -4) 3 C) y = 4 3 x - 4; slope: 4 ; y-intercept: (0, -4) 3 D) y = 4 3 x + 12; slope: 4 ; y-intercept: (0, 12) 3 Use the slope-intercept form to write an equation of the line that passes through the given points. Use function notation where y = f(x). 16) (4, 5) and (2, 13) 16) A) f(x) = -4x + 11 B) f(x) = -4x - 21 C) f(x) = 4x + 11 D) f(x) = -4x

6 Find the slope of the secant line indicated with a dashed line. 17) 17) A) m = 4 7 B) m = 7 4 C) m = D) m = Determine the average rate of change of the function on the given interval. 18) f(x) = 2x on [1, 3] 18) A) 1 2 B) 8 C) 3 2 D) -8 Use the point-slope formula to write an equation of the line that passes through the given points. Write the answer in slope-intercept form (if possible). 19) Passes through (-5, 2) and the slope is undefined. 19) A) y = 2 B) y = x - 5 C) y = x + 2 D) x = -5 Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. 20) The line passes through the point (6, -14) and has a slope of ) A) y = 3x - 14 B) y = -3x - 14 C) y = -3x + 4 D) y = -3x + 6 Write an equation of the line satisfying the given conditions. Write the answer in standard form with no fractional coefficients. 21) Passes through (-5, -1) and is parallel to the line defined by 3x - 5y = 9 21) A) 3x - 5y = -6 B) 3x - 5y = -1 C) 3x - 5y = -5 D) 3x - 5y = -10 6

7 Use translations to graph the given function. 22) f (x) = x ) A) B) C) D) 7

8 Sketch the graph using transformations of a parent function (without a table of values). 23) r(x) = x ) A) B) C) D) 8

9 24) a(x) = (x - 1) 2 24) A) B) C) D) 9

10 Use translations to graph the given function. 25) a(x) = x ) A) B) C) D) 10

11 Solve the problem. 26) Use the graph of y = f (x) below to graph y = 2f (x) 26) A) B) C) D) 11

12 Graph the function by applying an appropriate reflection. 27) f(x) = - x 27) A) B) C) D) 12

13 Use transformations to graph the given function. 28) f(x) = -(x + 1) ) A) B) C) D) Determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, origin, or none of these. 29) y = -x 4 - x 2 29) A) origin B) x-axis C) y-axis D) none of these Find f(-x) and determine whether f is odd, even, or neither. 30) f (x) = -5x 5 + 4x 3 30) A) f (-x) = -5x 5-4x 3 ; f is odd. B) f (-x) = 5x 5-4x 3 ; f is odd. C) f (-x) = 5x 5-4x 3 ; f is even. D) f (-x) = 5x 5-4x 3 ; f is neither odd nor even. 13

14 Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. 31) 31) A) a. (-, 2) (2, ) b. never decreasing c. (-3, 1) C) a. (-5, ) b. (-, -5) c. never constant B) a. never increasing b. (-, -3) (1, ) c. (-3, 1) D) a. (-, -3) (1, ) b. never decreasing c. (-3, 1) 14

15 Identify the location and value of any relative maxima or minima of the function. 32) 32) A) At x = -5.7, the function has a relative minimum of 0. At x = 0, the function has a relative maximum of 0. At x = 5.7, the function has a relative minimum of 0. B) At x = -4, the function has a relative minimum of 0. At x = 0, the function has a relative maximum of 0. At x = 4, the function has a relative minimum of 0. C) At x = -4, the function has a relative minimum of -5. At x = 0, the function has a relative maximum of 0. At x = 4, the function has a relative minimum of -5. D) At x = -4, the function has a relative minimum of -5. At x = 4, the function has a relative minimum of -5. Evaluate the function for the given value of x. f 33) f (x) = 4x, g(x) = x - 6, (2) =? 33) g A) f g (2) = 1 2 B) f g (2) = C) f g (2) = - 2 f D) g (2) = 2 34) f (x) = 5x, g(x) = -4x 2-7, (g - f )(x) =? 34) A) (g - f )(x) = -4x 2-5x + 7 B) (g - f )(x) = -4x 2 + 5x + 7 C) (g - f )(x) = -4x 2-5x - 7 D) (g - f )(x) = -4x 2 + 5x - 7 Find f(x + h) - f(x) h for the given function. 35) f (x) = x 2 + 2x. 35) A) 2x + 2 B) 2xh + h C) 2x + h + 2 D) 1 15

16 Evaluate the function for the given value of x. 36) f (x) = x 2 + 2x, g(x) = 5x - 1, (g f )(2) =? 36) A) (g f )(2) = 39 B) (g f )(2) = 72 C) (g f )(2) = 32 D) (g f )(2) = 99 Refer to the values of k(x) and p(x) in the table, and evaluate the function for the given value of x. 37) x k(x) p(x) (p k)(-1) A) -5 B) -2 C) -4 D) 1 Use the definition of a one-to-one function to determine if the function is one-to-one. 38) f (x) = x ) A) Yes B) No A one-to-one function is given. Write an expression for the inverse function. 39) f (x) = 5x ) A) f -1 (x) = x B) f -1 (x) = x ) C) f -1 (x) = 3 x D) f -1 (x) = x ) f (x) = x + 5 x - 1 A) f -1 (x) = 5 + 1x x - 1 C) f -1 (x) = 5-1x x + 1 B) f -1 (x) = x + 1 x - 5 D) f -1 (x) = x - 1 x ) 16

17 Answer Key Testname: UNTITLED1 1) A 2) A 3) B 4) A 5) A 6) B 7) C 8) D 9) A 10) D 11) D 12) C 13) D 14) C 15) C 16) D 17) B 18) B 19) D 20) C 21) D 22) C 23) D 24) C 25) A 26) A 27) C 28) A 29) C 30) B 31) D 32) C 33) D 34) C 35) C 36) A 37) D 38) B 39) C 40) A 17