September 18, B Math Test Chapter 1 Name: x can be expressed as: {y y 0, y R}.

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1 September 8, B Math Test Chapter Name: Part : Objective Questions [ mark each, total 2 marks]. State whether each of the following statements is TRUE or FALSE a) The mapping rule (x, y) (-x, y) represents an x-axis reflection. b) The range of the function y x can be expressed as: {y y 0, y R}. c) y = 2x 3 reflected in the x-axis would result in the function y = -2x + 3. d) If y = f(x) is horizontally compressed by a factor of 0.25, the function would be changed to y = f(4x). e) The expressions x = f(y) and y = f - (x) both represent y-axis reflections of y = f(x). f) y 2x 4 represents a horizontal translation of y 2x of 4 to the right. 2. For each question, place the LETTER of the correct answer in the space provided. (i) Determine the equation of the transformed function. The basic function was y = x 2. A. y x 4 ² B. y x 4 ² C. y x 4 ² D. y 4x ² E. y x 7 4 ²

2 (ii) If the following point (-4, -0) is vertically expanded by a factor of 2, what are the coordinates of the image point? A. (-8, 0) B. (-4, -20) C. (-2, -0) D. (-4, -5) E. (-0, -4) (iii) As seen in the graph below, describe the type of reflection performed on the function y x 4. A. reflection over the y-axis B. reflection over the line y x C. reflection over both axes D. reflection over the x-axis (iv) Which one of the following descriptions, in the order presented, is correct in explaining how the transformation y 3 f (2x) can be obtained from y f (x). A. Vertical compression of 3, horizontal compression of 2, vertical translation down. B. Vertical expansion of 3, horizontal compression of 2, vertical translation down. C. Vertical translation down, vertical expansion of 3, horizontal expansion by 2. D. Vertical expansion of 3, horizontal expansion of 2, vertical translation down (v) The graph of y f (x) contains the point (3, 4). The point (3, 4) is transformed to (5, 5). Which of the following is a possible equation of the transformed function? A. y f ( x 2) B. y f ( x 2) C. y f ( x 2) D. y f ( x 2)

3 (vi) Given the graph y f (x) as the original function, what is the equation for g(x)? A. g( x) f ( x) 2 B. g( x) f ( x) 2 C. g( x) f ( 2x) D. g( x) 2 f ( x) E. g( x) 2 f ( x) Part 2: Written Problems [Total 38 points]. Determine the equation of the function g(x) after the indicated reflection. [2] a) y 3 ( x 6), in the x-axis g(x) = b) y x 2, in the y-axis g(x) = 2. Determine the equation of the inverse of the given function. Use proper notation for the final answer for the inverse function. [3] f x ( x ) 3

4 3. The following is the graph of y f (x). a) On the grid, sketch y = - f(x). [2] b) State any invariant point(s): [] c) Without graphing it, is the inverse of y = f(x) a function? [] d) What is the name of the test that tells you if the inverse is a function without actually graphing the inverse? [] 4. The following is the graph of y f (x). a) Sketch the graph of the inverse. [2] b) State the domain and range of the inverse. [2] Domain: Range:

5 5. Consider the function of y x in each case. [6]. Write the equation of the transformed function a) Translated 3 units to the left and translated 5 units down a) b) Vertically expanded by a factor of 5 and horizontally compressed by a factor of 3 b) c) Horizontal expansion (factor of 4), reflected in the x-axis. c) 6. A translation is performed on the point A (2, -5), moving it to A (-3,-). If the image of another point, B, under the same translation, is B (,4), what is the ordered pair of the original point B? Give answer only. No work is required to be shown. [] 7. Determine the equation of the inverse of f ( x) ( x 4)². [3] 8. You are given the function f ( x) ( x 3)( x 5). [3] a) What are the zeros of this function? b) What are the zeros of the transformed function, y f ( x)? c) What are the zeros of the transformed function, y f ( x)? 3

6 9. Given the graph y f (x), sketch the graph of y 2 f ( x 8) 3 on the same grid. [3] 0. Given y f (x), sketch y f ( x ) 6. Given y f (x), sketch y f ( x 2) on the same grid. [3] on the same grid. [4]. Find the inverse of the function 2x px ( ) 3 8x. All work must be shown. []