Question

Select the correct answer.

Consider the graph of rational function f.
f(x)
96
-6 -4
-2
6
4.
2
-2
-4
-6
0
2
Which equation represents function f?
4.
1
6
➤X

Answer 1

An equation that represents the rational function shown in the graph below is
`f(x)=(4x-8)/(x^(2) +x-6)`

Based on the graph of the rational function shown below, we can logically deduce the following key features;

Vertical asymptotes: x = -3 ⇒ (x + 2).

Horizontal asymptote: y = 0

Holes: x = 2 ⇒ (x - 2)

point = (-1, 2)

Therefore, when x = -3, the rational function becomes undefined;

`f(x)=(1)/(x+3) \\\\f(-3)=(1)/(-3+3)`

f(-3) = 1/0 (undefined).

Next, we would determine the value of a by using the pointt (-1, 2) as follows;

`f(x) = (a(x - 2))/((x + 3)(x - 2))\\\\2 = (a(-1 - 2))/((-1 +3)(-1 -2))\\\\2=(-3a)/(-6) \\\\12=3a\\\\a=(12)/(3)`

a = 4

In this context, an equation for the rational function graphed below can be written as follows;

`f(x) = (4(x - 2))/((x - 2)(x +3))\\\\f(x)=(4x-8)/(x^(2) +x-6)`

Complete Question:

Consider the graph of rational function f.

Which equation represents function?