# Lesson 4

Using Function Notation to Describe Rules (Part 1)

• Let’s look at some rules that describe functions and write some, too.

### Problem 1

Match each equation with a description of the function it represents.

### Problem 2

Function $$P$$ represents the perimeter, in inches, of a square with side length $$x$$ inches.

1. Complete the table.
 $$x$$ $$P(x)$$ 0 1 2 3 4 5 6
2. Write an equation to represent function $$P$$.
3. Sketch a graph of function $$P$$.

### Problem 3

Functions $$f$$ and $$A$$ are defined by these equations.

$$f(x)=80-15x$$

$$A(x)=25+10x$$

Which function has a greater value when $$x$$ is 2.5?

### Problem 4

An equilateral triangle has three sides of equal length. Function $$P$$ gives the perimeter of an equilateral triangle of side length $$s$$.

1. Find $$P(2)$$
2. Find $$P(10)$$
3. Find $$P(s)$$

### Problem 5

Imagine a situation where a person is using a garden hose to fill a child's pool. Think of two quantities that are related in this situation and that can be seen as a function.

1. Define the function using a statement of the form “$$\underline{\hspace{0.5in}}$$ is a function of $$\underline{\hspace{0.5in}}$$. Be sure to consider the units of measurement.
2. Sketch a possible graph of the function. Be sure to label the axes.

Then, identify the coordinates of one point on the graph and explain its meaning.

(From Unit 4, Lesson 1.)

### Problem 6

Function $$C$$ gives the cost, in dollars, of buying $$n$$ apples.

Which statement best represents the meaning of $$C(10)=9$$?

A:

The cost of buying 9 apples

B:

The cost of 9 apples is $10. C: The cost of 10 apples D: Ten apples cost$9.

(From Unit 4, Lesson 2.)

### Problem 7

Diego is baking cookies for a fundraiser. He opens a 5-pound bag of flour and uses 1.5 pounds of flour to bake the cookies.

Which equation or inequality represents $$f$$, the amount of flour left in the bag after Diego bakes the cookies?

A:

$$f = 1.5$$

B:

$$f < 1.5$$

C:

$$f = 3.5$$

D:

$$f > 3.5$$

(From Unit 2, Lesson 18.)