a.
To calculate the domain of the function
a.
Answer to Problem 53RE
Explanation of Solution
Given:
Function:
Concept used:
The domain of the function is the set of values, where the function is defined.
Calculation:
Now, finding the domain of the function,
When
So, the domain of the function is
Conclusion:
Hence, the domain of the function is
b.
To find the intercepts of the function
b.
Answer to Problem 53RE
(1.5, 0)
Explanation of Solution
Given:
Function:
Calculation:
Consider the function
To find the y-intercept, put
So, y-intercept does not exist.
To find the x-intercept, put
So, the x- intercept is (1.5, 0).
Conclusion:
Therefore, the x- intercept is (1.5, 0).
c.
To find the asymptotes to the function
c.
Answer to Problem 53RE
Explanation of Solution
Given:
Function:
Calculation:
Asymptotes:
Vertical asymptotes:
To find vertical asymptotes, put denominator of the given function equal to zero.
Horizontal asymptotes:
As the degree of numerator is equal to the degree of the denominator, the horizontal asymptote for given function is
Conclusion:
Therefore, the vertical asymptote is
d.
To sketch the function
d.
Explanation of Solution
Given:
Function:
Calculation for graph:
Consider
Values of x | Values of h(x) |
0 | Infinity |
1 | -1 |
-1 | 5 |
2 | 0.5 |
-2 | 3.5 |
By taking different values of x, the graph can be plotted.
Graph:
Interpretation:
The above graph represents the sketch of given function.
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
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