The function f(x)=log3xf(x)=log3⁡⁡x is transformed by the mapping statement f(x)→f(x−1)−1f(x)→f(x−1)−1. Part A: Will the transformation affect the intersection of f(x)f(x) and the line y=1y=1? Why Part B: Which graph illustrates this transformation, where f(x)f(x) is the preimage and g(x)g(x) is the image? Select one answer that correctly answers both questions in Part A and select one answer for Part B.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.4: More Quadratic Functions And Applications
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The function f(x)=log3xf(x)=log3⁡⁡x is transformed by the mapping statement f(x)→f(x−1)−1f(x)→f(x−1)−1.

Part A: Will the transformation affect the intersection of f(x)f(x) and the line y=1y=1? Why

Part B: Which graph illustrates this transformation, where f(x)f(x) is the preimage and g(x)g(x) is the image?

Select one answer that correctly answers both questions in Part A and select one answer for Part B.

O B:
OA: Yes. The intersection changes because a translation of the graph changes the base.
DA: Yes. Because the transformation affects the entire graph, the intersection of
fx) and y = 1 will also be moved.
O A: No. The transformation does not affect the entire graph.
OA: No. Although the transformation will move the graph, it will not affect the x-
coordinates.
f(x)
g(x)
DA: No. Although the transformation will move the graph, it will not affect the y-
coordinates.
© 2017 FlipSwitch. Created using GeoGebra.
J B:
B:
O B:
5
-5
5
-5
5.
-5
g(x)/ | f(x)
f(x).
g(x)
-5
© 2017 FlipSwitch. Created using GeoGebra.
© 2017 FlipSwitch. Created using GeoGebra.
© 2017 FlipSwitch. Created using GeoGebra.
5.
Transcribed Image Text:O B: OA: Yes. The intersection changes because a translation of the graph changes the base. DA: Yes. Because the transformation affects the entire graph, the intersection of fx) and y = 1 will also be moved. O A: No. The transformation does not affect the entire graph. OA: No. Although the transformation will move the graph, it will not affect the x- coordinates. f(x) g(x) DA: No. Although the transformation will move the graph, it will not affect the y- coordinates. © 2017 FlipSwitch. Created using GeoGebra. J B: B: O B: 5 -5 5 -5 5. -5 g(x)/ | f(x) f(x). g(x) -5 © 2017 FlipSwitch. Created using GeoGebra. © 2017 FlipSwitch. Created using GeoGebra. © 2017 FlipSwitch. Created using GeoGebra. 5.
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