Question

What is the graph of the function f(x) = the quantity of x squared plus 5x plus 6, all over x plus 3?

Answer 1

Positive sloping linear graph with hole at negative 3, negative 1 intersecting the x axis at negative two and the y axis at two

Answer 2

Answer:

The graph of given function is shown below.

Step-by-step explanation:

The given function is

$f(x)=\frac{x^2+5x+6}{x+3}$

Factorize the numerator.

$f(x)=\frac{x^2+3x+2x+6}{x+3}$

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

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

Cancel out the common factor.

$f(x)=x+2$

It is a straight line because it is a one degree polynomial.

At x=0,

$f(0)=0+2=2$

The y-intercept of the function is (0,2).

Put f(x)=0

$0=x+2$

$x=-2$

The x-intercept of the function is (-2,0).

Equate the cancel factor equal to 0, to find the hole of the function.

$x+3=0\Rightarrow x=-3$

The function has hole at x=-3.

The graph of given function is shown below.