Question

Which situations represent linear functions? Check all that apply.

The temperature rises and falls over the course of a day. Temperature is a function of time.
A baseball is hit into the outfield. The height of the ball is a function of time.
A car goes 55 mph on the highway. Distance is a function of time.
A child grew 2 inches this year and 1 inch last year. Height is a function of time.
A movie director makes 2 movies per year. The number of movies is a function of the years.

Answer 1

Answer: c and e

Step-by-step explanation:

Answer 2

2 Answers:

Choice C and choice E

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Step-by-step explanation:

Choice A is ruled out because of the phrasing "rises and falls". A linear function can't do both rising and falling. You must only pick one direction to aim for. Choice B is ruled out for similar reasoning. A parabola is likely a better option for choice B.

Choice C is linear assuming the car stays at 55 mph. Recall that distance = rate*time. In this case, the equation is y = 55x where x is the number of hours and y is the distance traveled in miles. As an example, x = 10 hours leads to y = 550 miles traveled.

Choice D isn't linear. The increase of 2 doesn't match with the increase of 1. Linear functions must have the same amount of increase over the same time gap.

Choice E is linear and the equation is y = 2x, where x is the number of years and y is the number of movies made total. For example, at year x = 10, the director has made y = 2x = 2*10 = 20 movies total.

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If in doubt, graph the situation. If you get a straight line, then the equation is linear.