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.

​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.

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.

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.

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

​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

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!