NC.M1.F-IF.4: Interpret functions in context

A bug travels up a tree from the ground for 30 seconds. It travels fast at first and then slows down. It stops for 10 seconds, then proceeds slowly, speeding up as it goes. Which sketch best illustrates the bug’s distance, d, from the ground over the 30-second interval?

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A ball is thrown into the air with a speed of 32 feet per second. The function $ h = 32t - 16t^2 $ models the height of the ball after t seconds. How many seconds does it take for the ball to reach its maximum height?

• 0.75 seconds

• 1 second

• 2 seconds

• 4 seconds

The graph shown represents a jogger’s speed during her jog around her neighborhood. Which statement best describes what the jogger was doing during the 9 – 12 minute interval of her jog?

• She was standing still.

• She was increasing her speed.

• She was decreasing her speed.

• She was jogging at a constant rate.

A ball is thrown into the air from the edge of a 48-foot high cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds. For which interval is the ball’s height always decreasing?

• A 0 ≤ x ≤ 2.5

• B 0 < x < 5.5

• C 2.5 < x < 5.5

• D x ≥ 2

The graph below shows the amount of Amanda’s paycheck based on a 40 hour work week, plus her commission from sales. Amanda earns 50% of the total amount of sales that she makes. Which is the best interpretation of the y-intercept of the graph?

• A Amanda’s paycheck will be $100 when she makes no sales.

• B Amanda’s paycheck will be $0 when she makes $100 in sales.

• C Amanda’s paycheck will be $125 when she makes $50 in sales.

• D Amanda’s paycheck will be $150 when she makes $100 in sales.

The graph shows the relationship between the height of a ball, y, thrown into the air and time, x. Which statement best describes the height of the ball?

• The maximum height is 2 meters.

• The maximum height is 4 meters.

• The height is increasing for 2 seconds.

• The height is increasing for 4 seconds.

The graph shows the speed of a car that is driven through a town and then on a highway. During which of the following time intervals was the car stopped at a traffic light?

• between 0 and 1 minute

• between 1 and 2 minutes

• between 2 and 3 minutes

• between 3 and 4 minutes

The amount of profit a company makes from selling video games for x dollars is modeled by the function P(x) = -x^2 + 100x + 350,000. To the nearest dollar, what price gives the maximum profit?

• $40.00

• $45.00

• $50.00

• $55.00

The graph shows Ana’s distance from home on an afternoon hike. How far from home was Ana after hiking for 3 hours?

• 1.5 miles

• 2 miles

• 2.5 miles

• 4 miles

The height of a rocket, in feet, t seconds after it is launched is modeled by the function $ h(t) = -16t^2 + 125t + 24 $. Which interval has the largest change in height?

• Between 0 and 1 seconds

• Between 3 and 4 seconds

• Between 5 and 6 seconds

• Between 7 and 8 seconds