Lesson 7 Form Follows Function Practice Understanding

Ready

1.

Compare different characteristics of each type of function by filling in the cells of each table as completely as possible.

	$y = 4 + 3 x$	$y = 4 (3^{x})$
Type of growth
What kind of sequence corresponds to each model?
Make a table of values
Find the rate of change
Graph each equation. Compare the graphs. What is the same? What is different?
Find the $y$ -intercept for each function.

2.

Find the $y$ -intercepts for the following equations.

a.

$y = 3 x$

b.

$y = 3^{x}$

3.

Explain how you can find the $y$ -intercept of a linear equation and how that is different from finding the $y$ -intercept of an exponential equation.

Set

Decide which form of an equation will be the most efficient to use based on the given information.

Choices include:

Linear: slope-intercept form, point-slope form, recursive form

Exponential: explicit and recursive forms

4.

Jasmine has been working to save money and wants to have an equation to model the amount of money in her bank account. She has been depositing $$ 175$ a month consistently. She doesn’t remember how much money she deposited initially; however, on her last statement, she saw that her account has been open for $10$ months and currently has $$ 2,475$ in it. Create an equation for Jasmine.

Which equation form do you choose?

Write the equation:

5.

The table shows the number of rectangles created every time there is a fold made through the center of a paper. Use this table for each question.

Folds	Rectangles
$1$	$2$
$2$	$4$
$3$	$8$
$4$	$16$

a.

Find the number or rectangles created with $5$ folds.

Which equation form do you choose?

Write the equation:

b.

Find the number of rectangles created with $14$ folds.

Which equation form do you choose?

Write the equation:

6.

A heavy punching bag containing $90$ kilograms of sand has a small hole in the bottom. The punching bag loses $1.2$ kilograms of sand through the hole every hour. Write an equation to model the loss of sand every hour.

Which equation form do you choose?

Write the equation:

7.

Since Scott started doing his workout plan, Janet has been inspired to set herself a goal to do more exercise and walk a little more each day. She has decided to walk $10 meters$ more every day. On day $20$ , she walked $800 meters$ . How many meters will she walk on day $21$ ? On day $60$ ?

Which equation form do you choose?

Write the equation:

For each equation provided state what information you see in the equation that will help you graph it, then graph it.

8.

$y = 8 {(\frac{1}{2})}^{n}$

a.

What do you know from the equation that helps you to graph the function?

b.

Graph.

9.

$y = 5 (x - 2) - 6$

a.

What do you know from the equation that helps you to graph the function?

b.

Graph.

Go

Solve each equation. Justify your answer by identifying the property(s) you used.

10.

$3 x = 15$

11.

$x - 10 = 2$

12.

$- 16 = x + 11$

13.

$6 + x = 10$

14.

$6 x = 18$

15.

$- 3 x = 2$