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Chapter 2: Q. 29 (page 113)

Find the function that is finally graphed after each of the following transformations is applied to the graph of y=xin the order stated.

(1) Reflect about the x-axis

(2) Shift up 2 units

(3) Shift left 3 units

Short Answer

Expert verified

The function after all the transformation isy=-x+3+2

Step by step solution

01

Step 1. Given information

We have been given a functiony=x

02

Step 2. Use the first transformation

If the graph of y=f(x)is shifted up by 2units then y=f(x)+2.

So,

y=-x+2

For a function y=f(x), the reflection about the x-axis of the graph of the function is given by y=-f(x).

So,

y=-x

03

Step 3. Use the second transformation

If the graph of y=f(x)is shifted left by 3units then y=f(x+3)

So,

y=-x+3+2

If the graph of y=f(x)is shifted up by 2units then y=f(x)+2.

So,

y=-x+2

04

Step 4. Use the third transformation 

If the graph of y=f(x)is shifted left by 3units then y=f(x+3)

So,

y=-x+3+2

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