Comparing Slopes and Intercepts of Functions

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.

Jasmine compared the x-intercept of f(x) = 2x – 8 to the x-intercept of the function shown in the table.

What is the value of the larger x-intercept of the two functions?

• -8

• -2

• 4

• 16

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.

Jason compared the function f(x) = 20(1.2)^x to the function that fits the values in the table.

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).

Which statement is true about the function f(x) = 6x + 2 and the linear function that fits the values in the table?

• f(x) has the same slope as g(x).

• f(x) has the same y-intercept as g(x).

• f(x) has the same x-intercept as g(x).

• f(x) and g(x) are the same function.

How far is the y-intercept of the function that fits the values in the table, from the y-intercept of the function graphed?

• 1 unit

• 2 units

• 5 units

• 9 units

What is the slope for Function C?

• -2

• 1/2

• 3

• 0

Which statement below is true? (Hint slope is Y / X)

• The slope of Function A is greater then the slope of Function B

• The slope of Function A is less than the slope of Function B

• The slope of Function A is the same as the slope of Function B