Introduction to Chapter 3 Exploration
Copy this definition in your notebook: A linear function is a function for which the graph is a
line. Read the information. Then, complete each task.
We solved lots of linear functions last chapter.
Helpful things you will want to recall for this exploration:
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Domain: x-values hit by the graph / the inputs
Range: y-values hit by the graph / the outputs
x-intercept: where the function hits the x-axis
y-intercept: where the function hits the y-axis
positive: if the graph is above the x-axis (positive y-values)
negative: if the graph is below the x-axis (negative y-values)
increasing: the y-values get larger as the x-values get larger (going up a mountain)
decreasing: the y-values get smaller as the x-values get larger (going down a mountain)
Task #1 Lines that slant up
Analyze the function at the right.
(a) What is the domain? What is the range?
(b) What is the x-intercept? What is the y-intercept?
(c) Where is the function positive? Where is it negative?
(d) Where is the function increasing? Where is it decreasing?
Task #2 Lines that slant down
Analyze the function at the right.
(a) What is the domain? What is the range?
(b) What is the x-intercept? What is the y-intercept?
(c) Where is the function positive? Where is it negative?
(d) Where is the function increasing? Where is it decreasing?
Task #3 Horizontal Lines
Analyze the function at the right.
(a) What is the domain? What is the range?
(b) What is the x-intercept? What is the y-intercept?
(c) Where is the function positive? Where is it negative?
(d) Where is the function increasing? Where is it
decreasing?
Task #4 Vertical Lines
Analyze the function at the right.
(a) What is the domain? What is the range?
(b) What is the x-intercept? What is the y-intercept?
(c) Where is the function positive? Where is it negative?
(d) Where is the function increasing? Where is it
decreasing?
Task #5
True or False.
(a) A slanted line can have more than one x-intercept.
(b) A line is either always or never increasing.
(c) Two different lines can have the same x-intercept.
(d) Two different lines can have the same y-intercept.
(e) Two different lines can have the same x and y-intercept.
Task #6
Sketch a linear graph that fits each description.
(a) as x increases, y decreases
(b) has an x-intercept at (3,0) and a y-intercept at (0,5)
(c) is not a function (recall the vertical line test)
(d) has domain: all numbers and range: {5}
Task #7
Plot each point. Then see if you can draw a straight line through them.
(a)
(b)
-2
-4
-3
-5
0
-2
0
-1
3
1
2
5
6
4
5
10