Graphs of Functions Study Guide

Watch the video showing Mark's distance from home, and then identify what is happening at each point on the graph.

Fill in the blanks and circle the correct words to describe change in a graph. Straight sections on a graph represent _______________ relationships and show a rate of change that is [constant/not constant]. Sections of a graph that are not straight represent _______________ relationships and show a rate of change that is [constant/not constant]. For a graph showing a car's distance over time, the rate of change is the car's _______________. When the car is speeding up, the rate of change is shown on the graph as an upward _______________. When the car's speed is constant, the rate of change is shown as a ____________________.

• linear

• nonlinear

• speed

• slope

• horizontal line

Fill in the blanks and complete the steps to sketch the graph of a trip that has 3 parts. Sarah walks to Natalie's house. Sarah waits for Natalie. Sarah and Natalie walk back to Sarah's house. The variable for the y-axis is _____________________________________________. The variable for the x-axis is ____________.

Graph the first part of the trip: Sarah walks to Natalie's house. Start at the origin. This is the point when Sarah's distance from her house = _____ and time = _____. Assume Sarah walks at a constant pace. Draw a segment to represent this part of the trip.

Graph the second part of the trip: Sarah waits at Natalie's house. Sarah's distance from her house _________________________, but the time continues to increase. Draw a segment to represent this part of the trip. Your segment should start at the end of the last segment.

Graph the third part of the trip: Sarah and Natalie walk back to Sarah's house. As Sarah walks back home, the distance from her house will [increase/decrease]. When Sarah is back home, her distance from her house will be _____. Draw a segment to represent this part of the trip. Your segment should start at the end of the last segment.

A graph of distance over time may include straight-line sections and curved sections. Explain why a graph of a real-world scenario may include curved sections.

Identify two scenarios that could be represented by each graph. Include one that is not shown in the study.