MATH-AII Boulton Functions Review Exam not valid for Paper Pencil Test Sessions

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1 MTH-II oulton Functions Review Exam not valid for Paper Pencil Test Sessions [Exam I:G9SY6 1 If f (x ) = x 3 + x - 8, what is f (-8)? Which of the following functions does NOT have a range of only the real numbers greater than or equal to zero? f (x ) = 4 - x f (x ) = x - 4 f (x ) = x 4 f (x ) = log.x 3 Which is a zero of f (x ) = 6x + 5x - 6?

2 4 The graph of a function is shown on the grid. What appears to be the range of this function? {y y = 1,, 3, 4} {y y = 0,, 4, 6, 8} {y 1 < y < 4} {y 0 < y < 8} 5 x + 3 The domain of the function f (x ) = is all real numbers except x + 5x - 4-8, -3, 3-8, 3-3, What is the domain of g (x ) = log(x - 1)? {x x > 10} {x x > 9} {x x > 1} {x x > 0} 7 What is the domain of the function defined by the following equation? f (x ) = 1 x {ll non-zero real numbers} {ll real numbers less than zero} {ll real numbers} {ll real numbers greater than zero}

3 8 Which function of x appears to have two distinct real zeros? 9 Which of the following functions of x has the greatest number of roots in the complex number system? y = x 3 + x - 1 y = x + x y = -x + 3 y = x - 4x +

4 10 The graph of a 4th-degree polynomial is shown. Exactly how many real zeros does this function have? Which number is a zero of f (x ) = log (4x - 1)? Which number is a zero of f (x ) = 7x + 6x - 48?

5 13 Which is a zero of the function f (x ) = x - x - 4? 14 The graph of g (x ) = log (x ) has no x -intercept or y -intercept one x -intercept and no y -intercept two x -intercepts and no y -intercept one x -intercept and one y -intercept 15 irections: lick on a box to choose each ordered pair you want to select. You must select all correct ordered pairs. Identify each of the x - and y -intercepts of the function h (x ) = x 3 + 3x - 4x - 1. (-3, 0) (0, -) (-, 0) (0, 0) (0, -1) (0, ) (0, -3) (, 0) 16 The function f (x ) = (1 - x ) - 4 is decreasing throughout the interval -4 < x < - < x < 1-1 < x < 3 - < x < 17 Throughout which of the following intervals is f (x ) = (x - 1)(x - 4) only decreasing? - < x < 0 - < x < 1 1 < x < 4 < x < 4

6 18 What is the equation of the horizontal asymptote of the graph of the following equation? y = 6 y = 0 y = -4 y = -5 f (x ) = 6 (x - 5) Given: f (x ) = log (x - 16) + 15 What is the equation of an asymptote of the graph of the given functions? x = 16 y = 16 x = 15 y = 15 0 What is the equation of the horizontal asymptote of the graph of the following equation? y = 4 y = 0 y = -1 y = -10 f (x ) = 4 (x +1) Which of the following describes the end behavior of y = -x + bx + c as x approaches either positive or negative infinity? y approaches positive infinity y approaches negative infinity y approaches c y approaches -c b s x approaches negative infinity, which of the following describes the end behavior of f (x ) = -x 7 + bx 3 + c? f (x ) approaches c f (x ) approaches 0 f (x ) approaches positive infinity f (x ) approaches negative infinity

7 3 irections: lick on the correct answers. Point lies on the graph of f (x ) = 1 x +. Identify each true statement. The image of Point that lies on the graph of f -1 (x ) is (1, -). The point (3, ) lies on the graph of f -1 (x ). The point (4, -4) lies on the graph of f -1 (x ). The image of Point that lies on the graph of f -1 (x ) is (, -1). 4 Which function is the inverse of g (x ) = x ?

8 5 The graph of the function g is shown on the following grid. Which graph best represents the inverse of g? 6 If f (x ) = x 5 and g (x ) = - - 3x, which is f (g (x ))? -x 5-3x 7 x 5 -x - 3x 10 (- - 3x 10 ) 5 (- - 3x ) 5 7 If f (x) = x - 7x, what is the value of f (-4)? If f (x ) = x + 1 and g (x ) = 6x - 15, which polynomial is equivalent to g (f (x ))? 3 4x x - 9 4x 3-10x + 6x x - 80x + 101

9 9 Given: f (x ) = 4x 4-15 and g (x ) = x + 11 What is the value of g (f (x ))? 8x x 4-30x x x 4-4 8x If f (x ) = x + 3x and g (x ) = x, what is g (f (-1))? f (x ) = x - 1 g (x ) = 3x Given the functions defined above, the composite function g (f (x )) is equal to 6x - 3 6x - 3 6x - 1 5x Given f (x ) = -3x + 4 and g (x ) = x + 7, what is the value of g (f ())?

10 33 Which appears to be an x -intercept of the graph shown? Where does the graph of the function f (x ) = (x + 1)(x - ) cross the x -axis? (1, 0) and (-, 0) (-1, 0) and (, 0) (0, 0) (1, -)

11 35 Which is an apparent zero of the function graphed? What are the x-intercepts for the graph of y = x + 5x - 6? (1, 0) and (-6, 0) (0, 1) and (0, -6) (-1, 0) and (6, 0) (0, -1) and (0, 6)

12 37 polynomial function, P (x ), is graphed as follows. What is the apparent solution set for P (x ) = 0? {0, } {-4, 0} {-, } {-4} 38 Given: f (x) = (x - 4) - 1 What is the vertex of the graph for this function? ( 4, 1) ( -4, 1 ) ( -4, -1 ) ( 4, -1 )

13 39 Which graph most likely represents a function with a zero of 5? 40 Which is a zero of the function f (x )= (x + 3)(x - 1)(x + )? polynomial function has a zero at x = 3. Which of the following expressions must be one factor of the polynomial? x 3 3x (x + 3) (x - 3)

14 4 Which graph best represents a function with zeros of -, -1, and? 43 Which of the following describes the root(s ) of the equation 9x = 6x - 1? Exactly one real root Two distinct real roots Exactly one imaginary root Two distinct imaginary roots 44 irections: lick on all the correct answers. Identify all the points where the graph of h (x ) = (x + 1)(x + 8x + 16) intersects the x -axis. (-4,0) (1, 0) (-, 0) (4, 0) (-1, 0) (16, 0)

15 45 For which set of data would the equation for the curve of best fit most likely be linear?

16 46 Which graph most accurately represents the function f (x ) = -x 3 + 3? 47 What is the number of turning points in the graph of the function of x defined below? y = x + 5x - 7

17 48 The graph of a parent function is shown. What function belongs to this same family? [Loading Figure] 49 y = x - 8x + 15 What are the x-intercepts of the graph that represents the equation? (0, -8) and (0, 15) (-8, 0) and (15, 0) (0, 3) and (0, 5) (3, 0) and (5, 0)

18 50 The graph shown most accurately represents which of the following functions? 51 What type of function is y = x + 8? Linear Exponential Step Quadratic

19 5 The graph most accurately represents which of the following functions? 53 The height of an object when projected upward can be described by the equation h = 70t - 4.9t, where h is height and t is time. The relationship between the height of the object and the elapsed time is an exponential function a step function a linear function a quadratic function