Answer:
- x-intercept: 1/2
- y-intercept: 1
- horizontal asymptote: y=2
- vertical asymptote: x=1
Explanation:
y-intercept
To find the y-intercept, set x=0 and solve for y.
y = 1/(0 -1) +2 = -1 +2
y = 1
x-intercept
To find the x-intercept, set y=0 and solve for x.
0 = 1/(x -1) +2
0 = 1 +2(x -1) . . . . multiply by x-1
1 = 2x . . . . . . . . . add 1, simplify
1/2 = x . . . . . . . . divide by 2
horizontal asymptote
This is the value of y as x gets very large. When that happens, the fraction with x in the denominator approaches zero, so the value of y approaches 2.
The horizontal asymptote is y = 2.
vertical asymptote
This is the value of x that makes the denominator zero.
The vertical asymptote is x = 1.