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

We have to graph the function f(x) which is represented as:

`f(x)=(x^2+5x+6)/(x+3)`

We can write the function f(x) as:

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

i.e. we get the equation of function f(x) as a linear function with x-intercept at (-2,0) and y-intercept at (0,2).

so, the graph of function f(x) is a straight line passing through (0,2) and (-2,0).

Answer 2

Given:

f(x) = (x2 + 5x + 6)/(x+3)

Required:

type of graph

Solution:

The function given can be simplified further. By factoring x2 + 5x + 6, we get (x+3)(x+2). Dividing it by (x+3), we are left with f(x) = x+2.

Therefore, the plot is a linear plot with a positive slope of 1 and a y-intercept of 2.