Ask a New Question
Menu

se the image to answer the question.

A piecewise linear function consisting of three parts is plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Time in minutes, and the y-axis is labeled Distance in miles.

Interpret the key function of the graph for the domain interval 9<t<14
. What scenario can be represented by this portion of the piecewise function?

(1 point)
Responses

a cyclist taking a cool down ride at a slower constant pace
a cyclist taking a cool down ride at a slower constant pace

a runner sprinting at a constant rate starting at minute nine
a runner sprinting at a constant rate starting at minute nine

a runner resting for 5 minutes
a runner resting for 5 minutes

driving a car at a constant rate for five hours
driving a car at a constant rate for five hours
Skip to navigation

3 answers

To interpret the key function of the graph for the domain interval \(9 < t < 14\), we need to consider the nature of a piecewise linear function within that interval.

Given that the context involves motion over time (with time in minutes and distance in miles), if the graph is linear between \(t = 9\) and \(t = 14\), it suggests a constant rate of change. If the line is horizontal during this interval, it indicates that there is no change in distance over time, which can represent a situation where the cyclist, runner, or driver is either resting or moving at a constant rate.

Based on the provided options, the best interpretation of the piecewise function for the interval \(9 < t < 14\) would be:

  • A runner resting for 5 minutes

This choice fits the context of a horizontal section of the graph where the distance does not change while time progresses.

Use the image to answer the question.

A step function consisting of four line segments is plotted in quadrant 1 of a coordinate plane.

The cost for shipping by the Boston Mailing Company is based on the amount that a customer spends. For customers spending under $50, the shipping rate is $10; for $50 to under $100, the shipping rate is $7; for $100 to under $140, the shipping rate is $4; for $140 and over the shipping rate is $2. What domain interval will have a shipping rate of $4?

(1 point)
Responses

50≤s<100
50 less than or equal to s less than 100

100<s≤140
100 less than s less than or equal to 140

100≤s<140
100 less than or equal to s less than 140

100<s<140
100 less than s less than 140

To determine the domain interval that will have a shipping rate of $4, we can look at the shipping cost details provided. According to the shipping rates:

  • For customers spending under $50: shipping rate is $10
  • For customers spending $50 to under $100: shipping rate is $7
  • For customers spending $100 to under $140: shipping rate is $4
  • For customers spending $140 and over: shipping rate is $2

From the information, the interval where the shipping rate is $4 corresponds to spending amounts from $100 to under $140.

Thus, the correct answer for the domain interval with a shipping rate of $4 is:

  • 100 ≤ s < 140

This means that the spending must be between $100 (inclusive) and $140 (exclusive).