Interpreting Rate of Change and Initial Value

Let's
Review....

Multiple Choice

Is the relation a function? Why or why not?

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

Multiple Choice

Which of these sets is not a function?

• { (2,3) , (3,5) , (4,9) }

• { (2,3) , (2,5) , (4, 9) }

• { (2,3) , (3,3) , (4,9) }

Multiple Choice

Is this is a function or not a function?

• Function
• Not a Function

Interpreting Rate of Change and Initial Value of Functions

​Functions

A function is a relationship between two quantities that can be represented by a graph, table, and equation.

y = 25x+60

​

Bonnie has decided to join a gym.

Fabulous Fitness charges $45 per month.

Greg’s Gym charges $99 at the end of three months.

Open Ended

Bonnie has decided to join a gym for the next 3 months.
Fabulous Fitness charges $45 per month.
Greg’s Gym charges $99 at the end of 3 months.

What strategies could Bonnie use to more easily compare the costs of the two gyms?

​Bonnie continues to research gym options and finds out that Fabulous Fitness has no sign-up fee, while Greg’s Gym charges $50 to sign-up.

​Take a minute to examine the information before answering the next few questions.

​She makes the following table to help her compare the two options.

Fill in the Blanks

Fill in the blank:

According to the graphic, Bonnie would need to pay $

to join Fabulous Fitness.

Click on the picture if you need to review it once more.

Fill in the Blanks

Fill in the blank:

According to the graphic, Bonnie would need to pay $

to join Greg's Gym.

Click on the picture if you need to review it once more.

The initial value represents the starting value of a function.

Initial Value

Fabulous Fitness has an initial value of 0 because they do not charge a sign-up fee.

Greg's Gym has an initial value of 50 because they charge a sign- up fee of $50.

Fill in the Blanks

Fill in the blank:

According to the graphic,

For the first 3 months at Fabulous Fitness, it costs $

per month.

(Type your answer in digits, not words)

Fill in the Blanks

Fill in the blank:

At Greg's Gym it costs $

per month, for the first 3 months.

(Type your answer in digits, not words)

The rate of change represents the value at which the function increases or decreases at a constant rate.

Rate of Change

Fabulous Fitness has a rate of change of 45 because they charge $45 per month.

Greg's Gym has a a rate of change of 33 because when split evenly between 3 months, it costs $33 per month.

Multiple Choice

If the data for each gym was graphed on a coordinate plane, which gym would have a point on the origin (0,0)?

• Fabulous Fitness

• Greg's Gym

The owner of Fabulous Fitness wants to buy name tags for her staff.

She writes the following function to represent the cost, y, for a certain number of name tags, x.​

​y = $2.00x + $7.00

Multiple Choice

What is the rate of change (CROC) for the cost of each tag based on the equation?

y = $2.00x + $7.00

• $2.00 per tag

• $7.00 per tag

Multiple Choice

What do you think is the initial value for the cost of the name tags based on the equation?

y = $2.00x + $7.00

• $2.00

• $7.00

​Cost of Name Tags

The graph shows how the cost of the name tags for the equation

y = 2.00x + 7.00


x represents the number of tags purchased

y represents the total cost

Fill in the Blanks

Take a look at the point on the graph which can be represented by the ordered pair (10,

).

---

What would be the correct y-value of the ordered pair?

Remember it costs $2 per tag plus the $7 initial fee.

As a reminder, when an equation is written slope-intercept form, the "m" represents the slope/CROC

Now we know that the "b" represents the y-intercept or the "initial value" of the function.

Slope-Intercept Form

OR

INITIAL VALUE!

OR

rate of change!