Compare Linear Functions

Compare Linear Functions

Open Ended

Which company shows a greater rate of change?

Open Ended

Which panda is growing faster?

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Compare the rates of change. Do they have the same rate of change? If they have different rates of change, which one is greater?

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Who weighed more at the beginning of the show?

Open Ended

Who is losing weight faster?

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Rich is a member of a gym. He pays a monthly fee plus a per-visit fee. The equation below represents the monthly amount Rich pays for his membership to the gym per month for x visits.

y = 3x + 10

What does the y-intercept (b) of the graph of this equation represent?

Open Ended

Charlie rented a moving truck. He paid a daily fee plus a per-mile fee to rent the truck. The equation below represents the daily amount Charlie paid for the truck if he drives it x miles.

y = 1/2x + 10

What does the slope (m) of the graph of this equation represent?

Open Ended

Equation A: y = 2x + 3

Equation B: y = 3x - 3

Which equation has a higher slope?

Open Ended

Equation A: y = 3x - 1

Equation B: y = 1/2x + 1

Which equation has a higher y-intercept?

Open Ended

What is the rate of change (slope) to rent a raft from Water's Edge Rafts?

Open Ended

What is the rate of change (slope) to rent a raft from Ryan's Rafts?

Open Ended

Which company shows a greater rate of change?

Multiple Choice

• The slope of Function A is greater than the slope of Function B.

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

Multiple Choice

which statement is true?

• The slope of Function A is greater than the slope of Function B.

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

Multiple Choice

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.

Multiple Choice

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.

Multiple Choice

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

Multiple Choice

The function h(t) represents the height in inches of a plant after t weeks. What does the notation h(4) = 5 mean?

• After 5 week the plant is 4 inches tall
• The plant grows at a rate of 5/4 inch per week
• After 4 weeks the plant is 5 inches tall
• The plant grows at a rate of 1 inch per week

Multiple Choice

What does f(1990)=214 mean in the context of the problem?

• In 1990 there were 214 million people with health insurance

• In 214, there were 1990 people with health insurance

• When there are 1990 people, the year is 214

• None of these