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://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=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T010900Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2b44e230a3029886091b9992bacc41e35d66e40a997427b4d80b737986dba0c5)
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T010900Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b5e06e9156867b1d89a9598ccea18d84feaeec7cf9565e4b9cb3537c41d244f2)
- 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://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=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T010900Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=da4dc5a53189367be5cb0f1340bcd827da4b4087cc692c7056c9d929aed3e9c8)
-
When was the bike rider going the fastest?
-
When was the bike rider going the slowest?
-
During what times was the rider going away from the beginning of the trail?
-
During what times was the rider going back towards the beginning of the trail?
-
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?