Question

What is the graph of the function f(x) = the quantity x squared minus 9x plus 20 over the quantity x minus 4?

Answer 1

Please see the attachment for graph.

Explanation:

Given:
`f(x)=(x^2-9x+20)/(x-4)`

It is rational function and need to draw the graph of function.

We have to find some parameters of function like hole, Vertical asymptote, Horizontal asymptote, x-intercept and y-intercept.

First we factor numerator and denominator, reduce the fraction.

`f(x)=(x^2-9x+20)/(x-4)\Rightarrow ((x-4)(x-5))/(x-4)=x-5`

1. Hole of the f(x) at x=4 because (x-4) cancel out from numerator and denominator. (4,-1)

2. Horizontal Asymptote: No horizontal asymptote (DNE)

3. Vertical Asymptote: No vertical Asymptote (DNE)

4. x-intercept: Put y=0 and solve for x. x-intercept = (5,0)

5. y-intercept: Put x=0 and solve for y. y-intercept = (0,-5)

Using above information we will draw the graph. Please see the attachment for graph.

Hence, The graph in attachment.