Concept explainers
(a)
To Draw:
A table of values where x is all integers from -5 to 5 , inclusive.
(a)
Explanation of Solution
Given Information:
Concept Used :
Absolute Value Function:
An absolute value function is a function that contains an algebraic expression within absolute value symbols. The absolute value of a number is its distance from 0 on the number line. Parent Function :
Domain : All real numbers
Range : All non-negative real numbers
Graph :
Calculation:
Make a table :
x | 2x | |
-5 | -10 | 13 |
-4 | -8 | 11 |
-3 | -6 | 9 |
-2 | -4 | 7 |
-1 | -2 | 5 |
0 | 0 | 3 |
1 | 2 | 5 |
2 | 4 | 7 |
3 | 6 | 9 |
4 | 8 | 11 |
5 | 10 | 13 |
(b)
To Plot :
The points of the table on a coordinate grid.
(b)
Explanation of Solution
Given Information:
From part (a)
x | |
-5 | 13 |
-4 | 11 |
-3 | 9 |
-2 | 7 |
-1 | 5 |
0 | 3 |
1 | 5 |
2 | 7 |
3 | 9 |
4 | 11 |
5 | 13 |
Graph:
Plot the points in the table on the graph:
(c)
To Graph :
The function.
(c)
Explanation of Solution
Given Information:
From part (b)
Graph:
Join the points with straight line :
We get the graph :
(d)
To Explain:
How this graph is different from the graph shown below :
(d)
Explanation of Solution
Given Information :
From part (c) and given , the two graph are :
Observation:
Merging the two graph :
The graph
When the constant is outside the absolute value symbol, the graph is shifted vertically. If the constant is inside the absolute value symbol, the graph is shifted horizontally.
Chapter 4 Solutions
Algebra 1
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