Lesson 6 Another Day Solidify Understanding

Ready

Solve the equations.

1.

$2.5 x = 40$

2.

$n - 12 = 29$

3.

$7 t + 15 = 36$

4.

$9 a + 10 = 91$

5.

The equation $12.5 t + 500 = 3, 500$ was created in connection with the following situation:

Jamie is considering a job opportunity that is offering a signing bonus of $$ 500$ and $$ 12.50$ per hour. He is hoping to earn $$ 3, 500$ before he returns to school in the fall.

a.

Solve for $t$ .

b.

If Jamie can work $40$ hours per week, how many weeks will it take to achieve his goal?

Set

6.

Graph the equations and label them:

$f (x) = 2 x + 7$
$g (x) = 2 x - 4$
$h (x) = 2 x + 3$

7.

Explain how $f (x)$ can be translated to be the same as $h (x)$ ?

8.

Explain how $g (x)$ can be translated to be the same as $f (x)$ ?

9.

Use the graph of $p (x)$ and the descriptions to graph $j (x)$ and $r (x)$ on the same grid.

Function, $j (x)$ comes from translating $p (x)$ up $5 units$ .
Function, $r (x)$ comes from translating $p (x)$ down $9 units$ .

10.

Use the graph of $f (x)$ and the descriptions to graph $g (x)$ and $h (x)$ on the same grid.

Function, $g (x)$ comes from translating $f (x)$ up $3 units$ .
Function, $h (x)$ comes from translating $f (x)$ down $6 units$ .

11.

If the graph of a function is translated either up or down to create a new function, how would this translation connect with equations of the two functions?

12.

Miriam remembers a saying that her uncle would always have when they asked him how he was doing. He would say, “I’m a day late and a dollar short.” She is always thinking mathematically and started wondering if this means at $- 1$ days he is in debt a dollar. She didn’t know if this made sense but made a table to show how she thought her uncle’s saying might be modeled mathematically.

Days	$- 1$	$0$	$1$	$2$	$3$
Dollars	$- 1$	$- 2$	$- 3$	$- 4$	$- 5$

a.

Create an explicit equation to model Miriam’s table.

b.

Create a graph to model this situation.

c.

If Miriam changes her model to show that her uncle actually had $ $10$ a day ago (so on day $- 1$ he has $$ 10$ ), how will this change the graph modeling the number of dollars he has?

Go

State the indicated features for each function and interpret the graph to answer the question.

13.

The graph is a model for outside temperature at a high mountain location for a fourteen-hour period.

Domain:

Range:

Increasing:

Decreasing:

Max:

Min:

$x$ -int:

$y$ -int:

When is the hottest time of the day?

14.

The graph is a model for the amount of gasoline in the tank of a large cargo truck during a day of travel.