# Lesson 1Function Family ReunionSolidify Understanding

Graph the equations on the corresponding grid.

### 1.

The graph of is shown.

#### a.

Graph the equations on the grid provided.

#### b.

For each new equation, explain what the number does to the graph of . Identify what changes in the graph and what stays the same. Pay attention to the -intercept, the -intercept(s), and the rate of change.

### 2.

The graph of is shown.

#### a.

Graph the equations on the grid provided.

#### b.

For each new equation, explain what the number does to the graph of . Identify what changes in the graph and what stays the same. Pay attention to the -intercept, the -intercept(s), and the rate of change.

## Set

Sketch the graph of the parent function and the graph of the transformed function on the same set of axes.

, and

, and

, and

,

and

,

and

### 8.

Use the graph and the table to write the rule for each of the different transformations of the parent graph represented in the columns labeled image 1 and image 2. Write the transformation rule as a geometric transformation of the original image, using the set of coordinate points, and then write the rule using algebraic function notation. Graph image 1 and image 2 on the same set of axes. (It’s possible that not all of the transformed points will fit on the given set of axes.)

Graph of parent function:

 pre-image (parent function) image 1 image 2 geometric notation $\left(x,y\right)$ $\left(x,y\right)\to$ $\left(x,\underset{―}{\phantom{\rule{2cm}{0ex}}}\right)$ $\left(x,y\right)\to$ $\left(\underset{―}{\phantom{\rule{2cm}{0ex}}}\right)$ function notation $f\left(x\right)={x}^{3}$ ${f}_{1}\left(x\right)=$ $\underset{―}{\phantom{\rule{2cm}{0ex}}}$ ${f}_{2}\left(x\right)=$ $\underset{―}{\phantom{\rule{2cm}{0ex}}}$ selected points that fit this image $\left(-2,-8\right)$ $\left(-2,-3\right)$ $\left(-4,64\right)$ $\left(-1,-1\right)$ $\left(-1,4\right)$ $\left(-3,27\right)$ $\left(0,0\right)$ $\left(0,5\right)$ $\left(-2,8\right)$ $\left(1,1\right)$ $\left(1,6\right)$ $\left(-1,1\right)$ $\left(2,8\right)$ $\left(2,13\right)$ $\left(0,0\right)$

## Go

Find the function values: , , and . Indicate if the function is undefined for a given value of .