Question

For the function f(x) = 2x-4/x+3
What is the x-intercept, y-intercept, and vertical asymptotes

Answer 1

x-intercept: (2,0)

y-intercept: (0,-4/3)

vertical asymptote: x = -3

Explanation:

To find the x-intercepts, we can set f(x) to 0, which is y=0:

2x-4/x+3 = 0

2x-4 = 0

2x = 4

x = 2

To find the y-intercepts, we can set x to 0:

2(0)-4/(0)+3 = y

y = -4/3

To find the vertical asymptote, we can set the denominator equal to 0:

x+3 = 0

x = -3