Multiple Graph Transformations - Extra Practice

Precalculus

Unit 2, Topic 2

Multiple Graph Transformations

Objectives and Vocabulary

•

You will:

•

Graph functions based on a combination of horizontal and

vertical transformations

•

Determine the rule of a function

𝑔

(

𝑥

)

based on a combination

of transformations applied to a given function

𝑓

(

𝑥

)

•

Investigate and analyze the effect of the order of

transformations

•

Key Terms:

Writing a Rule for Multiple Vertical OR Horizontal Transformations

To write the rule:

1. Determine the operations needed.

2. Determine the order the operations need to occur.

3. Write and simplify the function rule.

Multiple Choice

You are told that the function $$g\left(x\right)$$ is the result of shifting the graph of $$f\left(x\right)=x^2$$ up 7 units and then vertically stretching it by a factor of 3. What is the rule for $$g\left(x\right)$$ ?

• $$g\left(x\right)=3x^2+21$$

• $$g\left(x\right)=3x^2+7$$

• $$g\left(x\right)=7x^2+21$$

• $$g\left(x\right)=7x^2+3$$

Multiple Choice

You are told that the function $$g\left(x\right)$$ is the result of shifting the graph of $$f\left(x\right)=\left|x\right|$$ right 5 units and then horizontally stretching it by a factor of 4. What is the rule for $$g\left(x\right)$$ ?

• $$g\left(x\right)=\left|4x-5\right|$$

• $$g\left(x\right)=\left|4x+5\right|$$

• $$g\left(x\right)=\left|\frac{1}{4}x-5\right|$$

• $$g\left(x\right)=\left|\frac{1}{4}x+5\right|$$

Performing a Sequence of Transformations to Determine the Rule of a Function

Extra Example

Multiple Choice

The graph of $$f\left(x\right)=\left|x\right|$$ is vertically compressed by a factor of 1/2, compressed horizontally by a factor of 1/3, and then shifted up 6 units and left 9 units to arrive at the graph of $$g\left(x\right)$$ . What is the rule for $$g\left(x\right)$$ ?

• $$g\left(x\right)=\frac{1}{2}\left|3x+27\right|+6$$

• $$g\left(x\right)=\frac{1}{2}\left|3x+9\right|-6$$

• $$g\left(x\right)=\frac{1}{2}\left|\frac{1}{3}x-3\right|-6$$

• $$g\left(x\right)=\frac{1}{2}\left|\frac{1}{3}x-9\right|+6$$