Question

Rational Expressions and Equations Identify any vertical asymptotes or point discontinuities of each function.

Answer 1

Answer:

To find the vertical asympote or point of dicontinuities

Given function is,

$f(x)=\frac{4x}{x^2-16}$

On solving the above equation, we get

$f(x)=\frac{4x}{(x-4)(x+4)}$

f(x) is not defined when x=4 and x=-4 (that is when denominator tends to zero)

we get,

The point of discontinuity is at x=-4 and x=4

Vertical Asymptote: ertical Asymptote - when x approaches any constant value c, parallel to the y-axis, then the curve goes towards +infinity or – infinity.

we get that,

$\lim _{x\to\pm4}f(x)=\lim _{x\to\pm4}\frac{4x}{x^2-16}=\pm\infty$

Vertical assymptote of f(x) is x=-4 and x=4