How do you graph f(x)=−3/(x−1) using holes, vertical and horizontal asymptotes, x and y intercepts?
iescabroussexg
Answered question
2022-09-12
How do you graph using holes, vertical and horizontal asymptotes, x and y intercepts?
Answer & Explanation
Karma Estes
Beginner2022-09-13Added 11 answers
Holes: since nothing was cancelled out, there are no holes.
Vertical Asymptote: Use the denominator. The function is undefined when the denominator is zero. At what value of x will the denominator equal zero?
Set the denominator to zero, and then solve for x.
x - 1 = 0 x = 1
The vertical asymptote will be at x = 1.
Horizontal Asymptote: Use the degrees of the numerator and denominator.
1. If the degree of the numerator is less than the degree of the denominator, HA is at y=0. 2. If the degree of the numerator is more than the degree of the denominator, there is no HA. 3. If they are equal, divide the coefficient of in the numerator by the coefficient of in the denominator.
The degree of the numerator is zero. The degree of the denominator is 1. The HA is at y=0.
x-int: The graph will pass through the x-axis when y is equal to zero.
Set y = 0, then solve for x.
In this case, this is not possible, therefore there is no x-intercept.
y-int: The graph will pass through the y-axis when x is equal to zero.
Set x = 0, then solve for y.
y=3
The graph passes through the y-axis at 3.
Use these values to plot points, then use a table of values if extra points are needed.