How to determine the end behavior of a rational function

Asked by admin @ 11/11/2021 in Mathematics viewed by 252 People

State the domain and end behavior of each rational function. Identify all horizontal and vertical asymptotes on the

graph of each rational function. Then, verify your answer by graphing the function on the graphing calculator.
1. f(x) = −x + 6 / 2x + 3
2. f(x) = 3x − 6 / x
3. f(x) = 3 / x2 − 25
4. f(x) = x2 − 2 / x2 + 2x − 3
5. f(x) = x2 − 5x − 4 / x + 1
6. f(x) = 5x / x2 + 9

Answered by admin @ 11/11/2021

Answer:

Rational Functions

Step-by-step explanation:

$f(x) = - \frac{x + 6}{2x + 3}$

• State the domain

X ∈ R : $x \neq - \frac{3}{2}$

• End Behaviour

$x \rightarrow \infty , y \rightarrow -\frac{1}{2}$

• Horizontal and Vertical

$y= -\frac{1}{2} , x=-\frac{3}{2}$

• Graphic (Annex)

2) $f(x) = \frac{3x − 6}{x}$

• State the domain

X ∈ R : $x \neq 0$

• End Behaviour

$x \rightarrow \infty , y \rightarrow 3$

• Horizontal and Vertical

$y= 0$

• Graphic (Annex)

3) $f(x) = \frac{3}{x^2-25}$

• State the domain

X ∈ R : $x \neq 5.5$

• End Behaviour

$x \rightarrow +/-\infty , y \rightarrow 0$

• Horizontal and Vertical

$y= 0 , x=+/- 5$

• Graphic (Annex)

4) $f(x) = \frac{ x^2-2}{x^2+2x-3}$

• State the domain

X ∈ R : $x \neq (3,1)$

• End Behaviour

$x \rightarrow +/-\infty , y \rightarrow +/- 1$

• Horizontal and Vertical

$y= 1 , x= (-3,1)$

• Graphic (Annex)

5) $f(x) = \frac{ x^2 − 5x − 4}{x + 1}$

• State the domain

X ∈ R : $x \neq -1$

• End Behaviour

$x \rightarrow +/-\infty , y \rightarrow +/ \infty$

• Horizontal and Vertical

$y=none , x= -1$

• Graphic (Annex)

6) $f(x) = \frac{ 5x }{x^2 + 9 }$

• State the domain

X ∈ R

• End Behaviour

$x \rightarrow +/-\infty , y \rightarrow 0$

• Horizontal and Vertical

$y= 0 , x= none$

• Graphic (Annex)

How to find the end behavior of a rational function

Asked by admin @ 05/11/2021 in Mathematics viewed by 293 persons

State the domain and end behavior of each rational function. Identify all horizontal and vertical asymptotes on the graph of each rational function. Then, verify your answer by graphing the …

What is the end behavior of the polynomial function

Asked by maham237 @ 20/05/2021 in Mathematics viewed by 294 persons

How to find end behavior of a function without graphing

Asked by admin @ 01/12/2021 in Mathematics viewed by 319 persons

Without graphing, describe the end behavior of the graph of the function. (Image provided includes function and answer options) *Please show all work, thanks.*

What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?

Asked by maham237 @ 02/12/2020 in Mathematics viewed by 432 persons

What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?

Asked by wiki @ 05/11/2020 in Mathematics viewed by 532 persons

What is the end behavior of the graph of the polynomial function f(x) = 2x3 – 26x – 24?

Asked by wiki @ 29/10/2020 in Mathematics viewed by 422 persons

How to determine the y intercept of a quadratic function

Asked by admin @ 26/11/2021 in Mathematics viewed by 290 persons

What is the y-intercept of this quadratic function? f(x)=-x2+10x-22

How to determine a function from a table of values

Asked by admin @ 26/11/2021 in Mathematics viewed by 278 persons

Given a table of values, how can you determine whether the function is linear, quadratic, or exponential?

How to determine if a function is one to one

Asked by admin @ 10/11/2021 in Mathematics viewed by 273 persons

Determine if the function is one-to-one. (5 points)

Which of the following is written as a rational function

Asked by maham237 @ 06/06/2021 in Mathematics viewed by 287 persons

A.G(x)=-2x B.P(x)=3x+4 C.Q(x)=x^2-8x+1 D.F(x)=x+2/5x

Analyze the function's graph to determine which statement is true

Asked by maham237 @ 21/05/2021 in Mathematics viewed by 435 persons

Over the interval [–2.5, 0.5], the local maximum is 2. As the x-values go to positive infinity, the function’s values go to negative infinity. The function is decreasing over the …

How do you determine if a relation is a function

Asked by maham237 @ 17/02/2021 in Mathematics viewed by 327 persons

Determine if the relation represents a function. Explain

End behavior notation

Asked by maham237 @ 12/01/2021 in Mathematics viewed by 293 persons

Write the domain and the range of the function as an inequality, using set notation, and using interval notation. also describe the end behavior of the function the graph of …

How to determine the minimum value of a quadratic function

Asked by maham237 @ 08/01/2021 in Mathematics viewed by 297 persons

How do you find the minimum value of a quadratic function?

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

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 370 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 …