Comparing Functions Given Value

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.

Suppose a bacteria is introduced to two different solutions in separate petri dishes. The bacteria in the first solution grow at a rate modeled by the function G(t) = (1.40)^t. The bacteria in the second solution grow in accordance with the data displayed in the table. Which statement best describes the growth rates exhibited within the two different solutions?

• The bacteria grow at the same rate in both solutions.

• The bacteria grow at a slower rate in the first solution.

• The bacteria grow at a faster rate in the first solution.

• The bacteria decay in the first solution and grow in the second solution.

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.

Dana and Dona made model rockets. Dana has Rocket 1 and Dona has Rocket 2. Both launch their rockets at the same time. If both rockets continue to increase in height at their same rates, which rocket will be the highest at 40 seconds. Rocket ​ (a)   will be higher, because it is a(n) ​ (b)   function. Rocket ​ (c)   is a(n) ​ ​ (d)   function.

• 1
• Exponential
• 2
• Polynomial
• Linear
• Absolute Value
• Piecewise

Which statement is true?

• A

• B

• C

• D

Which statement is TRUE about this graph?

• b(4) > r(4)

• b(1) > r(1)

• b(5) > r(5)

• b(-1) < r(-1)

• F
• G
• H
• J

Which statement below describes the comparison of the linear function f(x) and the exponential function g(x)?

• The value of g(x) is always greater than the value of f(x).

• The value of g(x) is never greater than the value of f(x).

• The value of g(x) will eventually exceed the value of f(x).

• There is not enough information to compare the value of f(x) to the value of g(x).

Which statement below describes the comparison of rate of change between the linear function f(x) and the exponential function g(x).

• g(x) rate of change is ALWAYS greater than f(x) rate of change.

• g(x) is NEVER greater than f(x) rate of change.

• g(x) will eventually exceed the rate of change of f(x).

• There is not enough information to compare the rate of change of f(x) to g(x).

Tags

TEKS.MATH.8.5C

Two new cars were purchased from Frank’s Auto Yard. Car A’s value n years after its purchase is found using the function P(n) = 13,500(0.83)ⁿ. Car B’s value in different years is shown in the table.

Using an exponential model, what is the approximate difference in the percent the two cars are depreciating?

• 17%

• 10%

• 7%

• 5%