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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 xvalue 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 xintercept 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 xintercept 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 xintercept of f ( x ) is 3. State the xintercept of y = f ⎜ ⎟
⎝4⎠
⎛x ⎞
The transformation y = f ⎜ ⎟ tells you to multiply the xvalues by 4
⎝4 ⎠
The new xintercept 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 xintercept
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 xintercept 1
f ( x) b) state the yintercept 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 = 21
y=1
c) sketch the function 15. The graph of y = f ( x ) is reflected in the yaxis 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 xintercepts at 6 and 1.
Where are the xintercepts 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.
 Spring '12
 A.Young
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