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Maths-

General

Easy

Question

Graph each function and identify the horizontal and vertical asymptotes
$straight F left parenthesis straight x right parenthesis equals to the power of x 2 minus 1$

hint Hint:

A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials such that q(x) ≠ 0.
Rational functions are of the form y=f(x)y = f x , where f(x)f x is a rational expression .

If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.

If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).

If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.

The correct answer is: From the graph we can analyze that the vertical asymptote of the rational function is x = −1 and x = 1 and horizontal asymptote is y = 0

Find the asymptotes of the rational function, if any.

Draw the asymptotes as dotted lines.

Find the x -intercept (s) and y -intercept of the rational function, if any.

Find the values of y for several different values of x .

Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
x² - 1= 0
x = 1 or x = -1
The vertical asymptote of the rational function is x=−1 and x= 1 .
This function has the x -intercept at (−14,0) and y -intercept at (0,4.167) . We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x =−1 and x = 1 and horizontal asymptote is y = 0

Related Questions to study

Write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to $y equals negative 2 over 3 x$ .

Write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to $y equals negative 2 over 3 x$ .

What is the graph of f(x $table attributes columnspacing 1em end attributes row cell 9 x squared minus 25 end cell row cell x squared minus 5 x minus 6 end cell end table$

What is the graph of f(x $table attributes columnspacing 1em end attributes row cell 9 x squared minus 25 end cell row cell x squared minus 5 x minus 6 end cell end table$

Direction : Fill in the blank with correct letter.
J _ _ p

Direction : Fill in the blank with correct letter.
J _ _ p

parallel

English-One-to-One

Direction : Identify the image and choose the correct word.

Direction : Identify the image and choose the correct word.

English-One-to-OneGeneral

Caroline loves reading history.
Which word is the gerund in the above sentence?

Caroline loves reading history.
Which word is the gerund in the above sentence?

Direction : Complete the following sentences by choosing suitable words:
The ____________ had a small birthday party celebration.

Direction : Complete the following sentences by choosing suitable words:
The ____________ had a small birthday party celebration.

parallel

Direction : Identify the root word’s meaning in Greek or Latin for the following word:
Folio, Foliage

Direction : Identify the root word’s meaning in Greek or Latin for the following word:
Folio, Foliage

Direction : Identify the root word’s meaning in Greek or Latin for the following word:
Autograph, Biography.

Direction : Identify the root word’s meaning in Greek or Latin for the following word:
Autograph, Biography.

Arrange the following in descending order :
$cube root of 17 comma space square root of 12 comma space cube root of 21 comma space square root of 18$

Arrange the following in descending order :
$cube root of 17 comma space square root of 12 comma space cube root of 21 comma space square root of 18$

parallel

Order the following from least to greatest :
$11 over 15 comma fraction numerator negative 5 over denominator 6 end fraction comma 3 over 4 comma fraction numerator negative 7 over denominator 9 end fraction$

Order the following from least to greatest :
$11 over 15 comma fraction numerator negative 5 over denominator 6 end fraction comma 3 over 4 comma fraction numerator negative 7 over denominator 9 end fraction$

Simplify $square root of 45 minus 3 square root of 20 plus 4 square root of 5$

Simplify $square root of 45 minus 3 square root of 20 plus 4 square root of 5$

Simplify by combining similar terms:
$2 cube root of 4 plus 7 cube root of 32 minus cube root of 500$

Simplify by combining similar terms:
$2 cube root of 4 plus 7 cube root of 32 minus cube root of 500$

parallel

Arrange in ascending order of magnitude :
$square root of 5 comma space cube root of 11 comma 2 times root index 6 of 3$

Arrange in ascending order of magnitude :
$square root of 5 comma space cube root of 11 comma 2 times root index 6 of 3$

Which is greater ?
$root index 6 of 3 comma space fourth root of 5 comma space square root of 2$

Which is greater ?
$root index 6 of 3 comma space fourth root of 5 comma space square root of 2$

Arrange the following from least to greatest :
0.1666666666...... , 1.66666666666.......... , 1.388888888888...............

Arrange the following from least to greatest :
0.1666666666...... , 1.66666666666.......... , 1.388888888888...............

parallel

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