Illustrative Math Algebra Functions

Function p represents the number of people in the museum on a Tuesday as a function of hours since the museum opened.

Here is the graph of function p.

Based on the graph and the situation, which domain and range make sense for function p?

• Domain: all numbers from 0 to 85. Range: all numbers from 0 to 14.

• Domain: whole numbers only from 0 to 14. Range: whole numbers only from 0 to 85.

• Domain: all numbers from 0 to 14. Range: whole numbers only from 0 to 85.

• Domain: whole numbers only from 0 to 14. Range: all numbers from 0 to 85.

To conduct an experiment, the room temperature in a lab needs to be as close as possible to -4 degrees Celsius. Any variation from this target temperature, whether warmer or cooler, is considered an error that could affect the experiment.

Function v gives the absolute temperature error as a function of the room temperature in degrees Celsius, x.

Select all statements that are true about the function and the situation.

• When the room temperature is 0 degrees Celsius, v(0) has a value of 4.

• When the room temperature is -5 degrees Celsius, the absolute temperature error, v(-5), is -1.

• When the room temperature is 1 degree Celsius, v(1) is 5.

• The equation v(x) = |x + 4| gives us the absolute temperature error when the room is x degrees Celsius.

• When v(x) = 0.5, the room temperature could be -3.5 or -4.5 degrees Celsius.

Here is the graph that represents a function

Which equation represents the function?

The equation m = 40g gives the distance in miles, m, that a car can travel using g gallons of gas.

If the car has gone 170 miles, how much gas was used?

• 3.5 gallons

• 4.25 gallons

• 4 gallons

• 6.5 gallons

The equation m = 40g gives the distance in miles, m, that a car can travel using g gallons of gas. Which equation represents the inverse function: the gallons of gas as a function of the distance in miles?

The cost of holding a children's birthday party at a rollerskating rink is a function of n, the number of people in the party. The cost function, C, can be represented with this set of rules.

How much does it cost to have a party with 15 people?

• $150

• $260

• $400

The cost of holding a children's birthday party at a rollerskating rink is a function of n, the number of people in the party. The cost function, C, can be represented with this set of rules.

How much does it cost to have a party with 12 people?

• $150

• $260

• $400

Function c is defined by the equation c(n) = 50 + 4n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n.

In this situation, what information would the inverse function give us?

• The number of visits

• How many gym visits if we know the monthly cost

• The cost of a membership

• The monthly cost if we know the gym visits

Function c is defined by the equation c(n) = 50 + 4n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n.

Find the inverse function.

Function c is defined by the equation c(n) = 50 + 4n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n.

Find the value of c(8) and explain what it means in this situation.

• $54; it means that 8 visits cost $54.

• $75; it means that 8 visits will cost $75.

• 8 visits will cost $62.

• 8 visits will cost $82.