To identify the parent function for the given graph, write the equation and describe the transformation for the graph.
Answer to Problem 29E
The equation is:
The parent function is:
Explanation of Solution
Given:
The given graph is:
After looking at the above graph the following can be concluded:
The given graph is a line.
x -intercept: The graph intersects the x -axis at about
y -intercept: The graph intersects the y -axis at about (0, 3). Hence the y -intercept is about 3.
Equation:
To write the equation of this line the intercept form which is:
Where, a is the x- intercept and b is the y- intercept.
Substituting the value of intercepts into the equation (i)
Hence, the obtained equation is:
Verification:
Using the graphing tool, the equation is plotted:
When the plotted graph and given graph are compared it is found that both the graphs are equal which means that the obtained equation is correct.
Parent function:
The obtained equation is:
Consider the function:
Hence, the parent function is:
Transformation Interpretation:
The function is:
Calculation for graph:
Consider
Values of x | Values of f (x ) |
0 | 3 |
-1 | 2 |
1 | 4 |
2 | 5 |
-2 | 1 |
Using the above table the graph can be plotted:
Calculation for graph:
Consider
Values of x | Values of g (x ) |
0 | 0 |
-1 | -1 |
1 | 1 |
2 | 2 |
-2 | -2 |
Using the above table the graph can be plotted:
Graph:
Interpretation:
Hence, comparing
The parent function is
Conclusion:
The obtained equation is
Chapter 1 Solutions
Precalculus with Limits: A Graphing Approach
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