Transformations Test

# Each of the following 8 6 4 2 8 6 4 2 2 4 6 8 2 4 6 8

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 4 2 -8 -6 -4 2 -2 4 6 8 -2 -4 -6 -8 a) y = f ( x + 2) − 3 (1 mark) b) y = f ( − 2 x ) (1 mark) 8 6 -4 4 2 -6 6 4 -8 8 2 2 -2 6 4 8 -8 -6 -4 2 -2 -2 -4 -6 -6 -8 -8 8 8 6 6 4 4 2 1 c) y = − f ( − 2 x + 4) + 1 (3 marks) 2 -8 -6 -4 8 -2 -4 6 4 2 -2 4 6 8 /2 2 d) y = f ( x ) (1 mark) -8 -6 -4 2 -2 -2 -2 -4 -4 -6 -6 -8 -8 4 6 8 e) y = 1 f ( x) + 1 2 f) y = f −1 ( x ) (1 mark) (2 marks) 8 6 -4 4 2 -6 6 4 -8 8 2 2 -2 6 4 -8 8 -6 -4 2 -2 -2 -4 -6 -6 -8 6 -2 -4 4 -8 8 6 4 1 /7 2 g) y = f ( x ) (3 marks) -8 -6 -4 2 -2 -2 -4 -6 -8 4 6 8 8 1 (2 marks) f ( x) h) y = −2 8 6 4 2 -8 -6 -4 2 -2 4 6 8 -2 -4 -6 -8 /6 Name:____________________ Date:____________________ Principles of Mathematics 12 – Transformations Test ( /33) Each multiple choice question is worth 1.5 marks. Clearly circle the best answer. No graphing calculators are permitted. 1. a) b) c) d) When compared to the graph of y = x 2 , the graph of y = ( x + 3) 2 − 2 has: vertical translation 3 units down, horizontal translation 2 units left vertical translation 2 units down, horizontal translation 3 units left vertical translation 2 units up, horizontal translation 3 units right vertical translation 2 units up, horizontal translation 3 units left 2. a) b) c) d) When y is replaced with − y , the graph is reflected over which line? the x–axis the y–axis the line y = x the line y = -x 3. a) b) c) d) How is the graph of y = 2 f ( x ) related to the graph of y = f ( x ) ? y = f ( x ) has been compressed vertically by a factor of 1/2. y = f ( x ) has been compressed horizontally by a factor of 1/2. y = f ( x ) has been expanded vertically by a factor of 2. y = f ( x ) has been expanded horizontally by a factor of 2. 4. of a) b) c) d) If the point (m, n) is on the graph of y = f ( x ) , what point is on the graph y = f −1 ( x ) ? (m, n) (-m, -n) (-n, -m) (n, m) /6 5. The function y = 9 − x 2 is expanded vertically by a factor of 2, reflected about the y – axis, and translated 3 units downward. The transformed function would be a) b) c) d) y = 2 9 − x2 − 3 y = 2 9 − x2 + 3 y = 2 9 + x2 + 3 y = 2 9 + x2 − 3 6. If (m, n) is a point on the graph of y = f ( x ) , determine a point on the graph of y = af ( bx ) − d . a) (am+d, bn) b) (m/b, an - d) c) (mb, n/a + d) d) (m/b, an + d) 7. If the graph of y = x 2 is horizontally compressed by a factor of ¼, and then reflected in the x – axis, determine an equation for the new graph. a) y = −16 x 2 b) y = −4 x 2 1 4 1 d) y = − x 2 16 c) y = − x 2 8. Which of the following transformations would reflect y = f ( x ) about the line y = x? a) y = − f ( x ) b) y = f ( − x ) c) y = f −1 ( x ) 1 d) y = f ( x ) /6 2x , find f −1 ( x ) . 3− x 3x a) f −1 ( x ) = 2+ x 9. Given y = 2+ x 3x x−2 c) f −1 ( x ) = 3x 2x d) f −1 ( x ) = x −3 b) f −1 ( x ) = 1 10. If the range of y = f ( x ) is − 2 ≤ y ≤ 3 , what will be the range of y = f ( x ) ? 1 1 2 3 1 1 b) − ≤ y ≤ 3 2 1 1 c) y ≤ − or y ≥ 2 3 −2 ≤ y ≤ 3 d) a) − ≤ y ≤ 11. If (-4, 12) is a point on the graph of y = f ( x ) , what must be a point on 1 2 the graph of y = − f (1 − x ) + 3 ? a) b) c) d) (5, -3) (5, 27) (3, -3) (3, 27) 12. How is the graph of y = f ( 2 x ) related to the graph of y = f ( x ) ? a) y = f ( x ) has been compressed vertically by a factor of ½ b) y = f ( x ) has been compressed horizontally by a factor of ½ c) y = f ( x ) has been expanded vertically by a factor of 2 d) y = f ( x ) has been expanded horizontally by a factor of 2 /6 Open Ended Section 1. Given the graph of y = f ( x ) , graph each of the following: 8 6 4 2 -8 -6 -4 2 -2 4 6 8 -2 -4 -6 -8 a) y = f ( x + 2) − 3 (1 mark) b) y = f ( − 2 x ) (1 mark) 8 6 -4 4 2 -6 6 4 -8 8 2 2 -2 6 4 8 -8 -6 -4 2 -2 -2 -4 -6 -6 -8 -8 8 8 6 6 4 4 2 1 c) y = − f ( − 2 x + 4) + 1 (3 marks) 2 -8 -6 -4 8 -2 -4 6 4 2 -2 4 6 8 /2 2 d) y = f ( x ) (1 mark) -8 -6 -4 2 -2 -2 -2 -4 -4 -6 -6 -8 -8 4 6 8 e) y = 1 f ( x) + 1 2 f) y = f −1 ( x ) (1 mark) (2 marks) 8 6 -4 4 2 -6 6 4 -8 8 2 2 -2 6 4 -8 8 -6 -4 2 -2 -2 -4 -6 -6 -8 6 -2 -4 4 -8 8 6 4 1 /7 2 g) y = f ( x ) (3 marks) -8 -6 -4 2 -2 -2 -4 -6 -8 4 6 8 8 1 (2 marks) f ( x) h) y = −2 8 6 4 2 -8 -6 -4 2 -2 4 6 8 -2 -4 -6 -8 /6...
View Full Document

## This note was uploaded on 09/30/2013 for the course MATH Principles taught by Professor Ms.boersma during the Fall '07 term at Canadian Hs.

Ask a homework question - tutors are online