# Lesson 1Growing RootsDevelop Understanding

A direct variation function is written as , where is a nonzero constant. The is called the constant of variation. If you rewrite as , you can see that is a constant ratio or a constant rate. The constant is also called the constant of proportionality.

Identify whether the given equation represents a direct variation function. If it does, state the constant of variation .

Yes/no?

?

Yes/no?

?

Yes/no?

?

### 4.

Yes/no?

?

State whether or not each table represents a direct variation relationship.

If it does, write the equation in form. How does form compare to form?

### 9.

#### a.

Select all graphs that show a direct variation function.

#### b.

Identify the features of a direct variation graph.

## Set

### 10.

Let be a continuous function. Make a table of values for . Then graph the function.

 $x$ $f\left(x\right)$ $0$ $0.5$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $16$

### 11.

The graph in problem 10 represents the square root function. Select all of the features that apply to the graph of the square root function. If you choose a feature that applies to the square root function, write the specific value(s) that describe the feature.

A.

-intercept

B.

-intercept

C.

Maximum

D.

Minimum

E.

Domain

F.

Range

G.

Contiuous

H.

Discrete

I.

Interval of increase

J.

Interval of decrease

K.

Constant rate of change

L.

Rate of change is constantly changing

### 12.

Explain why the domain of does not include negative numbers.

### 13.

Four secant lines have been drawn on the graph of . Find the average rate of change of between and the following points: , , , and . What do the different rates of change of the secant lines tell you about the rate of change of the square root function?

## Go

Describe the transformation on each parabola. Then graph the function.

Description:

Description:

Description:

Description: