Question
Asked Sep 27, 2019
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White a function based on the parent function y = xand transformation in given order:

a) shift 5 units to the left

b) Reflect across the y-axis

c) Shift upward 4 units

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Expert Answer

Step 1

Given:

The parent function y = x3.

Reflection
The graph of y f(-x) is the reflection of the graph of y f(x
across y -axis
Horizontal translation:
For d 0
The graph of y
f (x+ d) is the graph of y f(x) shifted to the
left d units
Veitical translation:
For d 0,
The graph of y f(x)+d is the graph of y f(x) shifted up d units
help_outline

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Reflection The graph of y f(-x) is the reflection of the graph of y f(x across y -axis Horizontal translation: For d 0 The graph of y f (x+ d) is the graph of y f(x) shifted to the left d units Veitical translation: For d 0, The graph of y f(x)+d is the graph of y f(x) shifted up d units

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Step 2

Now perform the following transformations in order as follows.

a)

3
The fun ction y (x+5) is shift of the function y xto
the left by 5 units
help_outline

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3 The fun ction y (x+5) is shift of the function y xto the left by 5 units

fullscreen
Step 3

b)

...
3
The function y (-x+5)is the reflection of the function y (x5
х+
across y — ахis.
help_outline

Image Transcriptionclose

3 The function y (-x+5)is the reflection of the function y (x5 х+ across y — ахis.

fullscreen

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