find the vertical asymptote for
a) $\displaystyle f(x)=\frac{1}{x^2-25}$
domain for
a) $\displaystyle f(x)=\frac{2x+3}{3x-4}$
range for
a) $\displaystyle f(x)=\frac{1}{x^2-9}$
horizontal asymptote for
a) $\displaystyle f(x)=\frac{4x-7}{x+8}$
Hi william,
For which values of x is f(x) undefined? Those will be your vertical asymptotes.
The denominator cannot = zero. What value would cause the denominator to = zero? Everything except that value would constitute the domain.
Another way of thinking about the horizontal asymptote. For very very large x (either positive or negative), each power of x is far larger than lower powers (example if x= 1000000, $\displaystyle x^2$ is 1000000 times as large and, $\displaystyle x^3$ is 1000000 times as large as that, etc. That is, for very large x, you can ignore all but the highest powers. For very large x, $\displaystyle \frac{4x- 7}{x+ 8}$ if very very close to $\displaystyle \frac{4x}{x}= 4$.
What do you mean, b and c? All of your problems are labeled "a"! Do you mean the domain and range questions?
For the domain, there are three ways to restrict it. Masters already mentioned one of them:
Now tell us the domain of $\displaystyle f(x)=\frac{2x+3}{3x-4}$ is.The denominator cannot = zero. What value would cause the denominator to = zero? Everything except that value would constitute the domain.
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