Lesson 1 Going to Pieces Develop Understanding

Ready

Use the graph to find the indicated function value.

1.

a.

$f (- 3) =$

b.

$f (- 2) =$

c.

$f (0) =$

d.

$f (2) =$

2.

a.

$g (0) =$

b.

$g (2) =$

c.

$g (3) =$

d.

$g (5) =$

3.

a.

$h (- 6) =$

b.

$h (0) =$

c.

$h (2) =$

d.

$h (7) =$

4.

a.

$r (- 2) =$

b.

$r (- 1) =$

c.

$r (0) =$

d.

$r (1) =$

5.

Isaac lives $3$ miles away from his school. School ended at $3 p.m.$ and Isaac began his walk home with his friend Tate, who lives $1$ mile away from the school, in the direction of Isaac’s house. Isaac stayed at Tate’s house for a while and then started home. On the way, he stopped at the library. Then he hurried home. The graph is a piecewise-defined function that shows Isaac’s distance from home during the time it took him to arrive home.

a.

How much time passed between school ending and Isaac’s arrival home?

b.

How long did Isaac stay at Tate’s house?

c.

How far is the library from Isaac’s house?

d.

Where was Isaac $3 hours$ after school ended?

e.

Use function notation to write a mathematical sentence expression that says the same thing as part d.

f.

When was Isaac walking the fastest? How fast was he walking?

Set

6.

A parking garage charges $$ 3$ for the first two hours that a car is parked in the garage. After that, the hourly fee is $$ 2$ per hour.

a.

Write a piecewise function $p (x)$ for the cost of parking a car in the garage for $x$ hours.

(The graph of $p (x)$ is shown.)

b.

What is the meaning of $p (1.5)$ for this situation?

7.

Lexie completed an $18$ -mile triathlon. She swam $1$ mile in $1$ hour, bicycled $12$ miles in $1$ hour, and then ran $5$ miles in $1$ hour.

$L (t) = {\begin{cases} t, & 0 \leq t \leq 1 \\ 12 t - 11, & 1 < t \leq 2 \\ 5 t + 3, & 2 < t \leq 3 \end{cases}$

a.

Create the graph of the piecewise function $L (t)$ .

b.

What is the meaning of $L (2.5)$ for this situation?

8.

Use the piecewise function showing the amount of money that will be charged, $c (p)$ , for a group to go to an amusement park based on the number of people, $p$ , in the group.

$c (p) = {\begin{cases} 65 p, & 0 \leq P \leq 10 \\ 55 p + 100, & 10 < p \leq 20 \\ 45 p + 300, & 20 < p \leq 30 \\ 35 p + 600, & 30 < p \end{cases}$

a.

Find $c (25)$ .

b.

Explain how each part of this statement fits with the situation.

$c (16) = 980$

c.

How much will it cost for a group of $23$ people to go to the park?

d.

How do you know which piece of the piecewise function to use when calculating the price for a given number of people?

Go

Use the given information to write the equation of the line in point-slope form. Graph each line.

9.

$p$ : $(1, 2)$ ; $m = 3$

Equation:

10.

$p$ : $(1, - 2)$ ; $m = - 1$

Equation:

11.

$p$ : $(5, - 1)$ ; $m = 2$

Equation:

Write the equation of the line, in point-slope form, that contains the given points. Then sketch the graph of each line.

12.

$K (0, 0); L (- 4, 5)$

Equation:

13.

$X (- 1, 7); Y (3, - 1)$

Equation:

14.

$T (- 1, - 9); V (5, 18)$

Equation: