Unit 8 Rate of Change and Linear Functions Quiz

What is the rate of change in the table shown below?

• 2/3

• 2

• 1/2

• 3

Answer explanation

A linear function has a rate of change of 3. Which of the following functions below could NOT represent this function?

• y = 3x + 1

• 
• y = x + 3

• 

Answer explanation

y=x+3 is the answer because it is the only response that does not have a slope of 3. We know this because there is not a 3 in front of the x.

What is the initial value of the table shown below?

• -1

• 1

• 0

• -2

Answer explanation

The initial value of the table is -2. This is found by taking the slope (3) and subtracting from 4 and then from 1 so that when x=0, y=-2.

What is the initial value of the function y = 3x - 5?

• A) 2

• B) -5

• C) 5

• D) 0

Answer explanation

The initial value of the function y = 3x - 5 is found by setting x=0. Therefore, y = 3(0) - 5 = -5. Hence, the correct answer is B) -5.

What is the initial value of the function 3y = 2x + 12?

• A) 4

• B) 5

• C) 12

• D) 2

Answer explanation

To find the initial value, set x = 0 in the equation 3y = 2x + 12. This gives 3y = 12, so y = 4. Therefore, the initial value is 4, which corresponds to option A.

What is the initial value in this situation:

A catering company charges a client $75 to book an event, then $55 per hour after.

• A) $55

• B) $75

• C) $130

• D) $20

Answer explanation

The initial value in this situation is $75, which is the amount charged by the catering company to book an event before any additional hourly charges.

Which function matches the table shown below?

• y = 3x + 6

• y = -3x + 6

• y = 6x + 3

• y = 1/3x + 6

Answer explanation

• 
• 
• 
• None of the above

Answer explanation

Which scenario is BEST represented by the graph shown?

• Tom is jogging in the park. He starts off slow, then picks up speed. He stops to rest on a bench, then resumes jogging, but has to slow down again to find his lost water bottle. After finding it, he sprints towards the finish line.

• Tom is jogging in the park. He maintains a steady pace throughout his jog, only stopping once at the halfway point to stretch before continuing at the same pace.

• Tom is jogging in the park. He starts with a quick pace, then slows down significantly as he gets tired. He stops completely to catch his breath, then walks slowly back to the starting point.

• Tom is jogging in the park. He begins his jog at a moderate pace, then gradually increases his speed throughout without stopping until he reaches the end of his route.

The graph below represents Mark's drive time on his way to work.

• Mark's car is stopped at intervals 2 and 5.

• Mark's car is increasing speed at intervals 2 and 4.

• Mark's car is decreasing speed at intervals 1, 3, and 5.

• Mark's car is driving faster in interval 4 than interval 3.

Answer explanation

Mark's car is stopped at intervals 2 and 5, as shown by the flat lines on the graph indicating no movement during those intervals.