Linear Functions and Distance vs Time Graphs

The distance vs time graph below shows the progress of 2 different runners during a race.

The graph shows that Runner B ran up a steeper path than Runner A.

• True

• False

The distance vs time graph below shows the progress of 2 different runners during a race.

Runner B increased their speed during the race.

• True

• False

The distance vs time graph below shows the progress of 2 different runners during a race.

Runner A and Runner B ran for the same amount of time.

• True

• False

• The population of yeast that doubles after every minute

• The height of a projectile after it is launched

• The distance covered by a car moving at a constant speed

• The cost of a printing machine that depreciates every year at 2% per year

• The number of members at the gym is best modeled a growing exponential function.

• The number of members at the gym is best modeled by a decaying exponential function.

• The number of members at the gym is best modeled an increasing linear function.

• The number of members at the gym is best modeled a decreasing linear function.

A student claims both of these graphs represent linear functions. Which statement is true?

• The student is incorrect because both graphs represent functions that change by a constant percent.

• The student is incorrect because only Graph 2 represents a function that changes by a constant rate.

• The student is incorrect because only Graph 1 represents a function that changes by a constant rate.

• The student is correct because both graphs represent functions that change by a constant rate.

• the amount of radioactive material with a decay rate of 3% every day

• the cost of a laptop that depreciates at the rate of 8% every year

• the height of the water in a tank when drained at the rate of 0.3 gallon per minute

• the amount of money in a savings account with an annual interest rate of 1.5%

A homeowner hires a carpenter for a project replacing kitchen cabinets. The homeowner pays a flat cost for materials, a price per hour, and tax.

Each cabinet costs $3.25 and the function H(x)=1.075(3.25x) represents the total cost of the handles.

Is this an example of exponential growth, decay, or linear?

• Exponential Growth

• Exponential Decay

• Linear

The distance vs. time graph below shows the progress of two different runners during a race. Mark each of the following statements as true or false.

• False

• The graph shows that Runner B ran up a steeper path than Runner A.

• False

• Runner A finished the race before Runner B.

• True

• Runner A and Runner B ran for the same amount of time.

• True

• Runner B increased his speed during the race.

• False

• Runner A and Runner B ran the same total distance.

A graphed line has a slope of -3 and passes through the point (-5, 11). Which equation represents the line?

• y = -3x + 11

• y = -5x – 3

• y = -3x – 4

• y = -5x + 11