Functions and Comparing Functions

Is this function linear or nonlinear?

• Linear

• Nonlinear

Is the graph pictured a linear or nonlinear function?

• Linear

• Nonlinear

Leonard compared the cost of purchasing a gallon of gas at two different gas stations. The function C(g) = 3.25 + 0.07x models the average cost of a gallon of gas at the first gas station after x months. The table below shows the average cost of a gallon of gas at the second gas station after different numbers of months. Which statement is true?

• The first station had a higher initial price per gallon and increased at a greater amount per month than the second station.

• The second station had a higher initial price per gallon and increased at a greater amount per month than the first station.

• The first station had a higher initial price per gallon but increased at a smaller amount per month than the second station.

• The second station had a higher initial price per gallon but increased at a smaller amount per month than the first station.

The table below shows some of the values for the linear function f.

Let g be the linear function defined by g(x) = 4x + 5.

Which statement is true?

• The graph of f has a greater slope than the graph of g.

• The graph of g has a greater slope than the graph of f.

• The graph of f has the same slope as the graph of g.

• The slopes of the graphs of f and g are undefined.

What is the approximate difference in the growth rates of the two functions?

• 0%

• 3%

• 5%

• 8%

Kaylee and Valerie invested money on the same day in accounts that earn compound interest. -- The function f(x) = 194(1.07)^x models the value of Kaylee’s account after x years. -- The table shows the value of Valerie’s account after different amounts of time. Which statement about the two accounts is true?

• Valerie initially invested $1 more than Kaylee.

• Kaylee initially invested $2 more than Valerie.

• Kaylee’s account is receiving an annual rate of 1 percentage point greater than Valerie’s account.

• Valerie’s account is receiving an annual rate of 2 percentage points greater than Kaylee’s account.

Marion compared the y-intercept of the function, f(x), shown in the table, to the y-intercept of the function, g(x), on the graph.

What is the distance between the y-intercepts of f(x) and g(x)?

• 0 units

• 4 units

• 12 units

• 20 units

What is the distance between the y-intercepts of the two functions?

• 14

• 8

• 6

• 4

The function C(m) = 0.55m + 3.75 models the cost to take an m mile-long taxi ride from Quick Cabs. The table shows the cost to take a cab different distances from Get You There Cabs. Which statement is true about the two cab companies?

• Quick Cabs costs less per mile but has a higher fixed fee than Get You There Cabs.

• Quick Cabs costs more per mile but has a lower fixed fee than Get You There Cabs.

• Quick Cabs costs less per mile and has a lower fixed fee than Get You There Cabs.

• Quick Cabs costs more per mile and has a higher fixed fee than Get You There Cabs.

Allison compared the y-intercept of f(x)= 4 – 5x to the y-intercept of the function that fits the values in the table.

Which statement is true?

• The y-intercept of g(x) is half the y-intercept of f(x).

• The y-intercept of g(x) is two times the y-intercept of f(x).

• The y-intercept of g(x) is equal to the y-intercept of f(x).

• The y-intercept of g(x) is the negative value of the y-intercept of f(x).