Writing the equation of a rational function given its graph

Asked by admin @ 05/11/2021 in Mathematics viewed by 361 People

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!

Answered by admin @ 05/11/2021

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:

$\mathbf{f(x) =\frac{x -1}{x +1}}$

(a) The vertical asymptote

Set the numerator to 0.

$\mathbf{x +1 = 0}$

Solve for x

$\mathbf{x = -1}$

Hence, the vertical asymptote is $\mathbf{x = -1}$

(b) The x-intercept

Set f(x) to 0

$\mathbf{\frac{x -1}{x +1} = 0}$

Multiply both sides by x = 1

$\mathbf{x -1= 0}$

Solve for x

$\mathbf{x =1}$

Hence, the x-intercept is $\mathbf{x =1}$

Set x to 0

$\mathbf{f(x) =\frac{0 -1}{0 +1}}$

$\mathbf{f(x) =\frac{-1}{1}}$

Solve for x

$\mathbf{f(x) =-1}$

Hence, the y-intercept is $\mathbf{f(x) =-1}$

See attachment for the graph of f(x)

Read more about intercepts and vertical asymptote at:

brainly.com/question/14770365

Determine the equation of the quadratic function from its graph

Asked by admin @ 22/11/2021 in Mathematics viewed by 379 persons

Find the equation of quadratic function determined from the graph below?

Which of the following rational functions is graphed below brainly

Asked by admin @ 15/10/2021 in Mathematics viewed by 376 persons

Which of the following rational functions is graphed below?

Which equation represents the graphed function.

Asked by maham237 @ 13/01/2021 in Mathematics viewed by 314 persons

Which equation represents the graphed function? A. –3x + 2 = y B. –x + 2 = y C. x – 3 = y D. 2x – 3 = y

The graph of a function f is given

Asked by maham237 @ 01/01/2021 in Mathematics viewed by 317 persons

The graphs of the function f (given in blue) and g (given in red) are plotted above. Suppose that u(x)=f(x)g(x) and v(x)=f(x)/g(x). Find each of the following: u'(1) = v'(1) …

Which equation represents the function graphed on the coordinate plane

Asked by maham237 @ 29/12/2020 in Mathematics viewed by 316 persons

Which equation represents the function graphed on the coordinate plane?

Choose the function whose graph is given below

Asked by maham237 @ 29/12/2020 in Mathematics viewed by 337 persons

Choose the function whose graph is given below.

Which of the following rational functions is graphed below

Asked by maham237 @ 29/12/2020 in Mathematics viewed by 344 persons

Which of the following rational functions is graphed below?

Which equation represents the graphed function

Asked by maham237 @ 28/12/2020 in Mathematics viewed by 296 persons

Which equation represents the graphed function? A. –3x + 2 = y B. –x + 2 = y C. x – 3 = y D. 2x – 3 = y

Use the given graph. determine the period of the function.

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 365 persons

Unit 6: Periodic Functions and Trigonometry Lesson 1: Exploring Periodic Data 1. Use the given graph. determine the period of the function. A. 4 B. -2.5 C. 2 D. 8 …