# Lesson 2

Function Notation

### Problem 1

The height of water in a bathtub, $$w$$, is a function of time, $$t$$. Let $$P$$ represent this function. Height is measured in inches and time in minutes.

Match each statement in function notation with a description.

### Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

### Problem 2

Function $$C$$ takes time for its input and gives a student’s Monday class for its output.

1. Use function notation to represent: A student has English at 10:00.
2. Write a statement to describe the meaning of $$C(11\!:\!15) = \text{chemistry}$$.

### Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

### Problem 3

Function $$f$$ gives the distance of a dog from a post, in feet, as a function of time, in seconds, since its owner left.

Find the value of $$f(20)$$ and of $$f(140)$$.

### Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

### Problem 4

Function $$C$$ gives the cost, in dollars, of buying $$n$$ apples. What does each expression or equation represent in this situation?

1. $$C(5)=4.50$$
2. $$C(2)$$

### Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

### Problem 5

A number of identical cups are stacked up. The number of cups in a stack and the height of the stack in centimeters are related.

1. Can we say that the height of the stack is a function of the number of cups in the stack? Explain your reasoning.
2. Can we say that the number of cups in a stack is a function of the height of the stack? Explain your reasoning.

### Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 4, Lesson 1.)

### Problem 6

In a function, the number of cups in a stack is a function of the height of the stack in centimeters.

1. Sketch a possible graph of the function on the coordinate plane. Be sure to label the axes.
2. Identify one point on the graph and explain the meaning of the point in the situation.

### Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 4, Lesson 1.)

### Problem 7

Solve each system of equations without graphing. Show your reasoning.

1. $$\begin{cases} \text-5x+3y=\text-8 \\ \hspace{1.5mm}3x-7y=\text-3 \\ \end{cases}$$

2. $$\begin{cases} \text-8x-2y=24 \\ \hspace{1.5mm}5x-3y=\hspace{3.5mm}2 \\ \end{cases}$$

### Solution

Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.

(From Unit 2, Lesson 16.)