Question
Let
This function has:
- Ay intercept at the point
-
intercepts at the point(s)
- Vertical asymptotes at
- Horizontal asymptote at
This function has:
Ask by Whittaker Daniel. in the United States
Nov 22,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
- y-intercept at
- x-intercepts at
and - Vertical asymptotes at
and - Horizontal asymptote at
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Beyond the Answer
To find the intercepts, asymptotes, and characteristics of the function
:
-
The
-intercept occurs when : So, the-intercept is at the point . -
The
-intercepts occur when the numerator equals zero . Factoring gives: Thus, the-intercepts are at the points and . -
For vertical asymptotes, set the denominator equal to zero:Using the quadratic formula:This gives
and . So, the vertical asymptotes are at and . -
For the horizontal asymptote, compare the leading coefficients of the numerator and denominator:Therefore, the horizontal asymptote is at
.
In summary:
-
-intercept at -
-intercepts at and - Vertical asymptotes at
and - Horizontal asymptote at