Question

Select the correct answer. Consider the function f(x)=x^2-3x/x^2-9. Which graph is the graph of function f?

Answer 1

Simplifying the function, it's graph is given at the end of this answer.

The function is:

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

The numerator can be factored as:

$x^2 - 3x = x(x - 3)$

Using subtraction of perfect squares, the denominator can be factored as:

$x^2 - 9 = (x + 3)(x - 3)$

Hence, the simplified function is:

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

Using a calculator, the graph is sketched at the end of this answer.

A similar problem, in which the graph of a function is found, is given at brainly.com/question/10389083