Lesson 6 Transformations of the Reciprocal Function

We will analyze transformations to the reciprocal parent function.
I will summarize the effects of a, b, c, and d values on the parent function.
TEKS 2A.6A

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Transformations of the Reciprocal Function

Fill in the Blanks

Look at the reciprocal parent function versus the transformed version! Notice where all the values landed.
We will talk more in-depth about this function later, for now we will practice transforming it.

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Switchin up the order now

​Notice the function is the only thing that has changed! The transformations themselves have remained constant and their placement (looks a little strange here) has also stayed the same.​

Here's our trusty table!

Graph 1 change corresponds to a being negative and graph 4 corresponds to b being negative.

The effect is the exact same, therefore when choosing which value to make negative, it doesn't really matter. Just pick one of them to make negative.

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Notice the effect on the graph between graph 1 and 4

Multiple Choice

If your equation looks like this: $$f\left(x\right)=-\frac{1}{x}$$ , which value is negative?

• a

• b

• both

• just one, it doesn't matter so we can pick whichever!

Complete the examples based off the table in your notes :)

Dropdown

In example A, the value a=​

Select answer

b=​

Select answer

c=​

Select answer

d=​

Select answer

How did you do?

Complete example B

Multiple Select

Select all that apply to example B.

• Reflected

• Vertically stretched

• Shifted up

• Shifted right

• Horizontally compressed

Did you get all the transformations?

Multiple Select

Select all that apply to example C.

• Reflected

• Vertically stretched

• Shifted up

• Shifted right

• Horizontally compressed

Math Response

What is the final equation? f(x)=_? (type only the equation only no f(x))

Type answer here

Correct Answer: \frac{1}{x-2.5}+6.5

Deg^°

Rad

Did you type it in correctly?

Math Response

What is the final equation? f(x)=_? (type only the equation only no f(x))

Type answer here

Correct Answer: -\frac{10}{x-3}-1

Deg^°

Rad

Did you notice it doesn't matter which value, a or b, we make negative?

Math Response

What is the final equation? f(x)=_? (type only the equation only no f(x))

Type answer here

Correct Answer: -\frac{10}{x-3}-1

Deg^°

Rad

Open Ended

Summarize the lesson below.