How do you graph f(x)=2x^2/x−3 using holes, vertical and horizontal asymptotes, x and y intercepts?
tidones0r
Answered question
2022-09-22
How do you graph using holes, vertical and horizontal asymptotes, x and y intercepts?
Answer & Explanation
edytorialkp
Beginner2022-09-23Added 10 answers
Let's find the holes of this formula. A hole means that the same factor is in the numerator as denominator and they divide out. Such as or so there is a hole when x=0. In our case of , there are no common factors, so there is no hole. Vertical asymptotes occur when we try to divide a value by 0. So let's see what value of x makes the denominator equal to 0: x−3=0 x=3 So, there is a vertical asymptote at x=3 Now let's see about the Horizontal asymptote. I like to use this to help me remember: BOBO - Bigger on bottom, y=0 BOTN - Bigger on top, none EATS DC - Exponents are the same, divide coefficients So in our case, the numerator (top) has a greater exponent (bigger). So there is no Horizontal asmptote (BOTN) Now let's find the x- intercepts and y- intercepts: x-intercept is the value of x when y equals 0:
x=0 The y-intercept is the value of y when x equals 0
y=0 Now we have all the information we need To check our answers, let's graph the equation graph{y=(2x^2)/(x-3)} We have an x and y intercept at 0, that's right. There's no horizontal asymptote although there is an asymptote for x=3 Our math is correct.