Question

Show all work to identify the discontinuity and zero of the function f of x equals 3 x over quantity x squared minus 9.

Answer 1

Answer:

Step-by-step explanation: 4x+2¥=12 Wittenberg in slope-intercept form

Answer 2

Answer:

Discontinuity: $x=-3$ and $x=3$.

Zero: $x=0$.

Step-by-step explanation:

We have been given a function $f(x)=\frac{3x}{x^2-9}$. We are asked to find the discontinuity of our given function.

We know that a function is discontinuous, when denominator of our given function will be 0.

$x^2-9=0$

$x^2-9+9=0+9$

$x^2=9$

Upon taking square root of both sides, we will get:

$x=\sqrt{9}$

$x=\pm 3$

Now, we will find zeros of our given function by substituting $y=0$ in our given function.

$0=\frac{3x}{x^2-9}$

$0(x^2-9)=\frac{3x}{(x^2-9)}(x^2-9)$

$0=3x$

$\frac{0}{3}=\frac{3x}{3}$

$0=x$

Therefore, our given function is discontinuous at points $x=-3$ and $x=3$. The zero of our given function is $x=0$.