The graphs of rational functions m and n have the same vertical asymptotes, and both have a single x-intercept at x = 5.
2 answers:
Answer:
A
Step-by-step explanation:
We are given two rational functions m(x) and n(x) that have the same vertical asymptotes both with a single x-intercept at x = 5.
The correct choice will be A.
Recall the transformations of functions.
B represents m(x) being shifted up 5 units. If the function is shifted up, the vertical asymptotes will be the same, but the x-intercept will change.
C represents m(x) being shifted 5 units to the right. This changes both the x-intercept and the vertical asymptotes.
Likewise, D represents m(x) being shifted 5 units to the left. Again, this will change both the x-intercept and the vertical asymptotes.
Therefore, the only choice left is A. It represents a vertical stretch by a factor of 5. This preserves the x-intercepts and the vertical asymptotes. Consider the function:
If n(x)=5m(x), we can see that:
So, the x-interceps and vertical asymptotes are preserved.
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You will have to use trig to solve this:
The side you have is adjacent to the known angle
The side you are looking for is opposite the known angle
^^^This means you need to use tan:
tan(24) =
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^^^input tan(24) into calculator, then multiply 12 to both sides to isolate and solve for x
5.3 ≈ x
Hope this helped!