Pre-Calculus Math 40s Standards Test - Transformations ANSWERS

Pre-Calculus Math 40s Standards Test - Transformations ANSWERS

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Unformatted text preview: Transformations Copyright © 2006, ANSWERS Transformations Standards TestBarry Mabillard. 0 www.math40s.com www.math40s.com 1. A point on the graph of y = f ( x ) is (-1, 2). State what this point will become in the graph of y = f ( − x ) Start with the given point (-1, 2) Multiply the x-value by a negative to obtain the answer (1, 2) 2. Given the function f ( x ) = x + 9 − 2 a) Find the equation of the inverse b) Sketch the original and inverse Rewrite as y = x + 9 - 2 Swap x & y x = y +9 - 2 Solve for y x + 2 = y +9 (x + 2 ) = y + 9 2 y = (x + 2 ) - 9 2 The inverse is 2 f -1 ( x ) = ( x + 2 ) - 9 c) Determine the x-intercept of f ( x ) d) Determine the domain of f ( x ) Set y = 0, then solve for x: 0 = x +9 - 2 The domain is { x | x ≥ -9} 2 = x +9 4 = x +9 x = -5 e) Determine the x-intercept of f −1 ( x ) f) Determine the domain of f −1 ( x ) Set y = 0, then solve for x: The domain is { x | x ≥ -2} 0 = (x + 2 ) - 9 2 9 = (x + 2 ) 2 ±3 = x + 2 → Reject - 3 since the original function doesn't exist for that x -value 3 = x+2 x=1 Transformations Standards Test ANSWERS 1 www.math40s.com 3. The graph of y = g ( x ) is shown to the right: Sketch: a) y = g ( x) b) y = − g ( x) c) y = g ( − x ) 4. The graph of f ( x ) = − x 2 − 1 is shown below. Draw the graph of y = 1 f ( x) ⎛ x⎞ 5. The x-intercept of f ( x ) is 3. State the x-intercept of y = f ⎜ ⎟ ⎝4⎠ ⎛x ⎞ The transformation y = f ⎜ ⎟ tells you to multiply the x-values by 4 ⎝4 ⎠ The new x-intercept is 12 Transformations Standards Test ANSWERS 2 www.math40s.com 6. Describe the transformations required to transform the graph of f ( x ) into g ( x ) . f ( x) g ( x) The transformations are: a vertical stretch by a factor of 2, then a shift of 2 units right and 2 units up. 7. The graph of y = f ( x ) is shown on the right. Sketch: a) y = − f ( x − 1) Transformations Standards Test ANSWERS b) y = 3 1 f ( x) www.math40s.com 8. Determine if the function f ( x ) = x − x 2 is even, odd, or neither. Evaluate f (-x ) f (-x ) = -x - (-x ) 2 f (-x ) = x - x 2 f (-x ) = f ( x ) The function is even ⎧ x 2 + 1, x > 0 ⎫ 9. Sketch the graph of f ( x ) = ⎨ ⎬ ⎩ 2 x, x ≤ 0 ⎭ 10. The graph of y = g ( x ) is shown below. The domain of y = 1 is g ( x) y = g ( x) There is a vertical asymptote in the reciprocal graph at the x-intercept of the original graph. The domain of the reciprocal is {x | x ≠ -2 } Transformations Standards Test ANSWERS 4 www.math40s.com 11. Given the graph of y = f ( x ) , sketch the following: 1 f ( x) 2 b) y = f ( 2 x ) c) y = − f ( x ) d) y = f ( − x ) a) y = 12. Sketch the graph of the following function if a) it’s an even function Transformations Standards Test ANSWERS b) it’s an odd function 5 www.math40s.com 13. Given the graph shown, sketch the graph of a) y = 2 f ( x − 1) b) y = 14. Given the function y = x + 4 − 1 a) state the x-intercept 1 f ( x) b) state the y-intercept Set y = 0, then solve for x: 0 = x+4 -1 Set x = 0, then solve for y: y = 0+4 -1 1= x + 4 1= x + 4 x = -3 y = 4 -1 y = 2-1 y=1 c) sketch the function 15. The graph of y = f ( x ) is reflected in the y-axis and shifted 3 units down. The equation of the transformation is: y = f (-x )- 3 Transformations Standards Test ANSWERS 6 www.math40s.com ⎧ x 2 + 1, x < 0 ⎫ ⎪ ⎪ 16. Sketch the function f ( x ) = ⎨ ⎬ and determine the value of f ( −3) ⎪ x, x ≥ 0 ⎪ ⎩ ⎭ To find the value of f (-3 ) , use the equation f ( x ) = x 2 + 1 since that is the graph present at x = -3. f (-3 ) = (-3 ) + 1 2 f (-3 ) = 9 + 1 f (-3 ) = 10 17. Given the graph of y = f ( x ) , draw the inverse and state the domain of the inverse the domain of the inverse is {x | x ∈ R} 18. Determine the value of the point (-2, 8) after the transformation y = Multiply the x - value by 1 f (2x) 4 1 1 and the y – value by . This gives (-1, 2) 2 4 19. The graph of f ( x ) = x 2 − 5 x − 6 has x-intercepts at -6 and 1. Where are the x-intercepts on the graph of y = ( x + 11) − 5 ( x + 11) − 6 2 The equation y = ( x + 11 ) - 5 ( x + 11 )- 6 is the same thing as f ( x + 11 ) 2 The graph is shifted 11 units left. The new values are -17 & -10 Transformations Standards Test ANSWERS 7 www.math40s.com ...
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This note was uploaded on 03/02/2012 for the course SCIENCE 1120 taught by Professor A.young during the Spring '12 term at Canadian University College.

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