To find the intercepts and test for symmetry, sketch the graph of the equation.
Answer to Problem 45E
The x-intercept is
Explanation of Solution
Given information:
The equation is
Test the symmetry:
Symmetry about x-axis.
Replace y with -y and get the function same as original.
Symmetry about y-axis.
Replace x with -x and get the function same as original.
Symmetry about origin.
Replace y with -y and x with -x, and get the function same as original.
Calculation:
For x-intercept,
Substitute
So, x-intercept is
For y-intercept,
Substitute
So, y-intercept is
Test the symmetry:
Symmetry about x-axis.
Replace y with -y.
Multiply by
The above function is different from original function.
So, there is no symmetry about x-axis.
Symmetry about y-axis.
Replace x with -x.
The above function is different from original function.
So, there is no symmetry about y-axis.
Symmetry about origin.
Replace y with -y and x with -x.
Multiply by
The above function is different from original function.
So, there is no symmetry about origin.
The values of the function y at the certain points.
x | -1 | 0 | 0.333 | 1 | 2 |
y = -3x + 1 | 4 | 1 | 0 | -2 | -5 |
The graph is shown below.
Chapter 1 Solutions
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