Asked by: Annelies Villoria
science space and astronomy

How do you find an asymptote of a graph?

Last Updated: 25th May, 2020

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The graph will have a vertical asymptoteat x=a if the denominator is zero at x=a and the numerator isn'tzero at x=a . If n<m then the x -axis is the horizontalasymptote. Ifn=m then the line y=ab y = a b is thehorizontal asymptote. If n>m there will be no horizontalasymptotes.

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Similarly one may ask, how do you find the horizontal asymptote of a graph?

Finding Horizontal Asymptotes of RationalFunctions

  1. If both polynomials are the same degree, divide thecoefficients of the highest degree terms.
  2. If the polynomial in the numerator is a lower degree than thedenominator, the x-axis (y = 0) is the horizontal asymptote.

how do you find the asymptotes of an exponential function? Certain functions, such as exponentialfunctions, always have a horizontal asymptote. Afunction of the form f(x) = a (bx) + c always hasa horizontal asymptote at y = c. For example, the horizontalasymptote of y = 30e6x –4 is: y = -4, and the horizontal asymptote of y = 5(2x) is y = 0.

Besides, how do you find the asymptote of an equation?

Vertical asymptotes can be found by solving theequation n(x) = 0 where n(x) is the denominator of thefunction ( note: this only applies if the numerator t(x) is notzero for the same x value). The graph has a verticalasymptote with the equation x = 1.

How do you define Asymptotes?

Asymptotes. An asymptote of a curve y=f(x)that has an infinite branch is called a line such that the distancebetween the point (x,f(x)) lying on the curve and the lineapproaches zero as the point moves along the branch to infinity.Asymptotes can be vertical, oblique (slant) andhorizontal.

Related Question Answers

Mehmood Derx

Professional

What are the rules for horizontal asymptotes?

The three rules that horizontal asymptotes follow are basedon the degree of the numerator, n, and the degree of thedenominator, m.
  • If n < m, the horizontal asymptote is y = 0.
  • If n = m, the horizontal asymptote is y = a/b.
  • If n > m, there is no horizontal asymptote.

Anatalia Neyenhaus

Professional

How do you find a vertical asymptote?

To find the vertical asymptote(s) of a rationalfunction, simply set the denominator equal to 0 and solve forx.

Alain Ibargarai

Professional

What is the horizontal asymptote?

A horizontal asymptote is a y-value on a graphwhich a function approaches but does not actually reach. Here is asimple graphical example where the graphed function approaches, butnever quite reaches, y=0 .

Jesper Garbett

Explainer

What is a vertical and horizontal asymptote?

The vertical asymptotes will occur at thosevalues of x for which the denominator is equal to zero: To find thehorizontal asymptote, we note that the degree of thenumerator is two and the degree of the denominator is one. Sincethe larger degree occurs in the numerator, the graph will have nohorizontal asymptote.

Zinedine Garayar

Explainer

What is vertical asymptote?

Vertical asymptotes are vertical lineswhich correspond to the zeroes of the denominator of a rationalfunction. (They can also arise in other contexts, such aslogarithms, but you'll almost certainly first encounterasymptotes in the context of rationals.)

Teonila Luchterhand

Explainer

What are horizontal lines?

A horizontal line is one which runs left-to-rightacross the page. In geometry, a horizontal line is one whichruns from left to right across the page. It comes from the word'horizon', in the sense that horizontal lines are parallelto the horizon. A vertical line is perpendicular to ahorizontal line.

Sanoussy Nejinsky

Pundit

Mihaita Domenico

Pundit

Why is an asymptote important?

Asymptotes convey information about the behaviorof curves in the large, and determining the asymptotes of afunction is an important step in sketching its graph. Thestudy of asymptotes of functions, construed in a broadsense, forms a part of the subject of asymptoticanalysis.

Clarena Holmsky

Pundit

How do you find the Y intercept?

To find the y intercept using the equationof the line, plug in 0 for the x variable and solve for y.If the equation is written in the slope-intercept form, plugin the slope and the x and y coordinates for a point on theline to solve for y.

Romaissae Leza

Pundit

What is a vertical asymptote and when does it occur?

f (x) = has vertical asymptotes of x = 2 and x =- 3, and f (x) = has vertical asymptotes of x = - 4 and x =. In general, a vertical asymptote occurs in a rationalfunction at any value of x for which the denominator is equal to 0,but for which the numerator is not equal to 0.

Boyana Uriburu

Teacher

What is asymptote of hyperbola?

A hyperbola with a horizontal transverse axis andcenter at (h, k) has one asymptote with equation y = k + (x- h) and the other with equation y = k - (x - h). Ahyperbola with a vertical transverse axis and center at (h,k) has one asymptote with equation y = k + (x - h) and theother with equation y = k - (x - h).

Lorenz Nowark

Teacher

How do you find the asymptotes of a hole?

Set each factor in the denominator equal to zero andsolve for the variable. If this factor does not appear in thenumerator, then it is a vertical asymptote of the equation.If it does appear in the numerator, then it is a hole in theequation.

Anju Magin

Reviewer

How find the range of a function?

Overall, the steps for algebraically finding the range of afunction are:
  1. Write down y=f(x) and then solve the equation for x, givingsomething of the form x=g(y).
  2. Find the domain of g(y), and this will be the range off(x).
  3. If you can't seem to solve for x, then try graphing thefunction to find the range.

Marharyta Tzagunov

Reviewer

What defines an exponential function?

An exponential function is a mathematicalfunction of the following form: f ( x ) = a x.where x is a variable, and a is a constant called the base of thefunction. The most commonly encounteredexponential-function base is the transcendentalnumber e , which is equal to approximately 2.71828.

Nishan Saklani

Reviewer

What is the equation for an exponential function?

Exponential Decay:
Remember that our original exponential formulawas y = abx. You will notice that in these new growthand decay functions, the b value (growth factor) has beenreplaced either by (1 + r) or by (1 - r). The growth "rate" (r) isdetermined as b = 1 + r.

Harol Scheungraber

Reviewer

What is an exponential function example?

Exponential Functions
In an exponential function, the independentvariable, or x-value, is the exponent, while the base is aconstant. For example, y = 2x would be an exponentialfunction.

Praxedes MaridueƱa

Supporter

How do you find the exponential function of a graph?

How To Find Exponential Functions
  1. Step 1: Solve for "a"
  2. Step 2: Solve for "b"
  3. Step 3: Write the Final Equation.
  4. Step 1: Find "k" from the Graph.
  5. Step 2: Solve for "a"
  6. Step 3: Solve for "b"
  7. Step 4: Write the Final Equation.

Florrie Imaoz

Supporter

How do you identify the domain and range of a function?

Another way to identify the domain and range offunctions is by using graphs. Because the domainrefers to the set of possible input values, the domain of agraph consists of all the input values shown on the x-axis. Therange is the set of possible output values, which are shownon the y-axis.

Tinatin Aubin

Beginner

What is exponential decay function?

In mathematics, exponential decay describes theprocess of reducing an amount by a consistent percentage rate overa period of time. It can be expressed by the formulay=a(1-b)x wherein y is the final amount, a is theoriginal amount, b is the decay factor, and x is the amountof time that has passed.