How do I graph the rational function: y=-6/x+4?
1 Answer
I like to identify the following things first, when asked to graph a rational function:
- y-intercept(s)
- x-intercept(s)
- vertical asymptote(s)
- horizontal asymptote(s)
-
To identify the y-intercept(s), ask yourself "what is the value of y when x=0"?
y = -6/0+4
Since6/0 is undefined, there is no y-int
y-intercept: none -
To identify the x-intercept(s), ask yourself "what is the value of x when y=0"?
0 = -6/x+4
-4 = -6/x
-4x = -6
x = -6/-4 = 3/2
x-intercept:(3/2,0) -
To identify the vertical asymptotes, we first try and simplify the function as much as possible and then look at where it is undefined
y = -6/x+4 is already simplified
Undefined whenx=0
Vertical asymptotes:x=0 -
To identify the horizontal asymptotes, we think of the limiting behavior (ie: what happens as x gets HUGE)
y = -6/"HUGE" +4 -> 0 + 4 -> 4
Horizontal asymptote:y=4
Now you might pick a couple additional points to the left/right of your horizontal asymptote to get a sense of the graph shape.
- Pick a point to the left of the
x=0 asymptote, ie:x=-6
y = -6/6 + 4 = -1 + 4 = 3
Point 1:(−6,3) - Pick a point to the right of the
x=0 asymptote, ie:x=6
y = 6/6 + 4 = 1 + 4 = 5
Point 2:(6,5)
Domain:
Range: