Answer:
- y-intercept: y = 3/4
- no x-intercepts
Step-by-step explanation:
To find the y-intercept, set x=0 and evaluate the function.
f(0) = -3/(0 -4) = 3/4
The y-intercept is (0, 3/4).
__
To find the x-intercept(s), set f(x) = 0 and solve for x.
0 = -3/(x^2 -4)
0 = -3 . . . . . . . . . . multiply by (x^2 -4), x ≠ ±2
There are no values of x that will make this true. There are no x-intercepts.
_____
Additional comments
In general, you find the x-intercepts of a rational function by finding the zeros of the numerator. Here, the numerator is -3, so cannot ever be zero.
I find a graphing calculator to be a useful tool for showing where to look for x-and y-intercepts. The attached graph shows y=0 (the x-axis) is a horizontal asymptote, so there are no x-intercepts.
