Question

Please Help,

Create a rational function with a linear binomial in both the numerator and denominator.

Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and intercepts.

Part 2. Show all work to identify the vertical asymptote, the x-intercepts, and the y-intercept.

Answer 1

Explanation:

Required is a graph of a rational function with degree 1 of x both in numerator and denominator also both binomials.

Consider the binomials x-1 and x+9

Let us consider f(x) =
`(x-1)/(x+9)`

This function graph is shown in the enclosure

2) Equate denominator to 0

We get x=-9

This is the vertical asymptote

For horizontal asymptote we see that both numerator and denominator have same degree

Hence horizontal asymptote is y = ratio of coefficients of leading terms

i.e.y=1 is horizontal asymptote

For x intercept put y =0

we get x =1 is the x intercept

For y intercept put x =0

y = 1/-11 = -1/11

Answer 2

f(x) = x−3 / x−5

x intercept = 3
y intercept = 0.6