Lesson 10
Piecewise Linear Functions
Let’s explore functions built out of linear pieces.
Problem 1
The graph shows the distance of a car from home as a function of time.
![Piecewise graph, horizontal, time, vertical, distance from home. Graph begins at the origin with a positive slope, then a horizontal segment, then a negative slope back to the horizontal axis.](https://staging-cms-im.s3.amazonaws.com/SVmue5KiufY9r4BHbyEd1Gh4?response-content-disposition=inline%3B%20filename%3D%228-8.5.PP.C.Image.06.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.PP.C.Image.06.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T133925Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b3002e15bc3987f115b4b9f6c7b7f3b9a83dde09c985a40694fd34b8a51623f5)
Describe what a person watching the car may be seeing.
Problem 2
The equation and the graph represent two functions. Use the equation \(y=4\) and the graph to answer the questions.
![A coordinate plane, x, negative 2 to 12 by ones, y, negative 2 to 7 by ones. A staright line through (negative 2 comma 0), (0 comma 1), (8 comma 5).](https://staging-cms-im.s3.amazonaws.com/sYUgcMPkb7PDYnLTDCR4dzju?response-content-disposition=inline%3B%20filename%3D%228-8.5.B7.PP.Image.102.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.B7.PP.Image.102.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T133925Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d13928fed32029203efdab796afe1686ef8a528e24924f591932b628a5fa2ac3)
- When \(x\) is 4, is the output of the equation or the graph greater?
- What value for \(x\) produces the same output in both the graph and the equation?
Problem 3
This graph shows a trip on a bike trail. The trail has markers every 0.5 km showing the distance from the beginning of the trail.
![Coordinate plane, x, time in hours, 0 to 3 point 4 by point 2, y, distance from beginning in kilometers, 0 to 10 by 2.](https://staging-cms-im.s3.amazonaws.com/bhrSDhFWxWmcEFGfziVJkexX?response-content-disposition=inline%3B%20filename%3D%228-8.5.C.PP.Image.15.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.C.PP.Image.15.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T133925Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=dd356918d434dc7d10e12981ba3adfca74687b3673b0b54a6d2635d33616cdaa)
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When was the bike rider going the fastest?
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When was the bike rider going the slowest?
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During what times was the rider going away from the beginning of the trail?
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During what times was the rider going back towards the beginning of the trail?
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During what times did the rider stop?
Problem 4
The expression \(\text-25t+1250\) represents the volume of liquid of a container after \(t\) seconds. The expression \(50t+250\) represents the volume of liquid of another container after \(t\) seconds. What does the equation \(\text-25t+1250=50t+250\) mean in this situation?