Task 3—Graphing Rational Functions 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.

THANKS!

Construct a simple function f(x) = (x+1) / (x-1);

Vertical asymptote: setting the denominator to 0 we get
x - 1 = 0 => x = -1

Horizontal asymptote: since the numerator and denominator have the same degree, simply divide the coefficients of the highest terms, which is 1, implies there's a asymptote at y = 1;

x-intersection: set f(x) to 0 => f(x) = 0 => x = -1;

y-intersection: set x to 0 => f(0) = -1 / 1 = -1;

Answer Link

chibuikeumeh chibuikeumeh · Answer 2 · 2021-10-21T21:38:03+02:00

The intercepts of a graph are the point where the graph crosses the x and y axes.

The vertical asymptote is x = -1
The x and y intercepts are x = 1 and y = -1, respectively.

The function is given as:

[tex]\mathbf{f(x) =\frac{x -1}{x +1}}[/tex]

(a) The vertical asymptote

Set the numerator to 0.

[tex]\mathbf{x +1 = 0}[/tex]

Solve for x

[tex]\mathbf{x = -1}[/tex]

Hence, the vertical asymptote is [tex]\mathbf{x = -1}[/tex]

(b) The x-intercept

Set f(x) to 0

[tex]\mathbf{\frac{x -1}{x +1} = 0}[/tex]

Multiply both sides by x = 1

[tex]\mathbf{x -1= 0}[/tex]

Solve for x

[tex]\mathbf{x =1}[/tex]

Hence, the x-intercept is [tex]\mathbf{x =1}[/tex]

(c) The y-intercept

Set x to 0

[tex]\mathbf{f(x) =\frac{0 -1}{0 +1}}[/tex]

[tex]\mathbf{f(x) =\frac{-1}{1}}[/tex]

Solve for x

[tex]\mathbf{f(x) =-1}[/tex]

Hence, the y-intercept is [tex]\mathbf{f(x) =-1}[/tex]

See attachment for the graph of f(x)

Read more about intercepts and vertical asymptote at:

https://brainly.com/question/14770365