A.3B Rate of Change

The table represents some points on the graph of a linear function. What is the rate of change of y with respect to x for this function?

• $\frac{2}{9}$

• $-\frac{9}{2}$

• $\frac{9}{2}$

• $-\frac{2}{9}$

Racer’s average driving speed for a 4-hour trip was 45 miles per hour. During the first three hours he drove 40 miles per hour. What was his average speed for the last hour of his

trip?

• 70 miles per hour

• 60 miles per hour

• 50 miles per hour

• 65 miles per hour

Look at the table. Which of the following best represents the situation in the table?

• If you rent a scooter for 8 hours you will pay $52.00.

• If two people each rented a scooter for 3.5 hours

  per day for 4 days, they would pay $164.00.

• If two people each rented a scooter for 1 hour each

  day for 2 days, they would pay $21.00.

• Not here.

The graph shows the volume of a gas sample as the temperature changes and the pressure remains constant. Which of the following best represents the rate of change in the volume of the gas sample with respect to the temperature?

• $\frac{7}{100}$ mL/C

• $\frac{1}{12}$ mL/C

• $12$ mL/C

• $22\ \frac{2}{5}$ mL/C

The graph shows the height of a tree every year. Which of the following is true about the rate of change of the tree's growth?

• The tree grew about 1 foot per year.

• The tree grew about 2 feet per year.

• The tree grew about 4 feet per year.

• The tree grew about 20 feet per year.

The table shows the price of a cup of yogurt with up to 5 toppings. What is the rate of change in price with respect to the number of toppings?

• $0.89 per topping

• $2.99 per topping

• $3.88 per topping

• $1.24 per topping

If y is a function of x such that 2x - 3y = 6, what is the rate of change of y with respect to x?

• -2

• $-\frac{3}{2}$

• $\frac{2}{3}$

• 2

Manuel lives 2 miles from the library and rides his bike there each day. He rides past one block every 50 seconds. If each block is 300 feet long, what is the rate, in feet per second, at which Manuel rides his bike?

• 6 feet per second

• 25 feet per second

• 60 feet per second

• 100 feet per second

The rate of change of two functions are being compared. One function, f(x) is represented by the equation

f(x) = -5x – 1, while the other function, g(x)

is represented in the table.

Which is true?

• The rate of change for f(x) is less than the rate of change for g(x).

• The rate of change for g(x) is less than the rate of change for f(x).

• The rate of change for f(x) and g(x) are equal.

• The rates of change cannot be compared because f(x) is a linear function and g(x) is an exponential function.

The graph of a linear function is shown in the coordinate plane. What is the rate of change in y per unit change in x for this linear function?

• -5

• -2.5

• -2

• -0.4