Question
(a) Find all
-intercepts and
-intercepts. Check all that apply.
-intercept(s):
-intercept(s):
(b) Write the equations for all vertical and horizontal
asymptotes. Enter the equations using the “and” button as
necessary. Select “None” as necessary.
Vertical asymptote(s):
Horizontal asymptote(s):
© Find the domain and range of
.
Write each answer as an interval or union of intervals.
Domain:
Range:
(b) Write the equations for all vertical and horizontal
asymptotes. Enter the equations using the “and” button as
necessary. Select “None” as necessary.
Vertical asymptote(s):
Horizontal asymptote(s):
© Find the domain and range of
Write each answer as an interval or union of intervals.
Domain:
Range:
Ask by Bryant Lee. in the United States
Mar 29,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
-
-intercept(s): -
-intercept(s): - Vertical asymptote(s): [Insert equations here]
- Horizontal asymptote(s):
- Domain:
- Range:
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Beyond the Answer
To find the
-intercepts, set
and solve for
. For
-intercepts, set
and solve for
. For example, if you have
, the
-intercepts are
and
and the
-intercept is
.
Vertical asymptotes occur where the denominator is zero (and not canceled by the numerator), while horizontal asymptotes depend on the degrees of the polynomials in the numerator and denominator. If the degree of the numerator is less than the denominator, the horizontal asymptote is
.
For the domain, identify all values of
that make the function valid. This usually excludes any
-values that make the denominator zero. The range typically requires analyzing the output values of the function, keeping an eye on limits and asymptotic behavior to ensure all possible outputs are covered.