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If a function has a vertical asymptote at a certain x-value then the function is at that value?
Undefined
How do you write an equation in slope intercept form when given x-intercept?
Since a vertical line goes straight up and down, its slope is undefined. Also, the x value of every point on a vertical line is the same. Therefore, whatever the x value is, is also the value of 'b'.x=bslope intercept form: y=mx+b
How do you find asymptotes?
Veritcal asymptotes are where the denominator of a fraction becomes 0 and the value of f(x) becomes undefined. Set the denominator to 0 and solve.Horizontal asymptotes are values of f(x) when x→∞ and x→-∞Two examples:f(x)=3x² / (x²+1)Vertical:Set (x²+1)=0 and solve for x.x²=-1 has no answers, so there is no vertical asymptote.Horizontal:Divide all terms by the highest power of x to eliminate unimportant valuesdividing by x², you get 3 / (1 + (1/x²))As x→∞ then 1/x² vanishes, leaving 3/1=3, so there is an asymptote at y=3f(x)=(x-3) / (x²+3x)Vertical:Set (x²+3x)=0 and solve. x={0,-3} so there are vertical asymptotes at 0 and -3Horizontal:Divide out by x²(x/x² - 3/x²) / (x²/x² + 3x/x²) as x→∞The terms in the numerator all vanish, making the answer 0, so there is a horizontal asymptote at 0.Enjoy.■A vertical asymptote also exists for the value of x (assuming a function of x) where the function becomes undefined. For instance:f(x) = ln (x). The logarithmic function is not defined for x
What is vertical asymptote?
A function y = f(x) has a vertical asymptote at x = c if,f(x) is continuous for values of x just above c and the value of f(x) becomes infinitely large or infinitely negative (but not oscillating between them) as x approaches c from above. The function could behave similarly as x approaches c from below.In such a case f(c) is a singularity: the function is not defined at that point.
How do you find an oblique asymptotes?
An oblique asymptote is another way of saying "slant asymptote."When the degree of the numerator is one greater than the denominator, an equation has a slant asymptote. You divide the numerator by the denominator, and get a value. Sometimes, the division pops out a remainder, but ignore that, and take the answer minus the remainder. Make your "adapted answer" equal to yand that is your asymptote equation. To graph the equation, plug values.
