How do you graph #f (v ) = \frac { 2v - 9} { 5v + 6}#?
1 Answer
Explanation:
Graphing
To graph a rational function (with algebra-only knowledge), we can find key features. These features are
- v- and y-intercepts (horizontal and vertical axis intercepts)
- holes
- asymptotes (vertical, horizontal, slant/oblique)
- end behavior and behavior around asymptote
v-intercept (horizontal axis intercept)
To find possible v-intercepts, set the function to equal zero to find the zeros.
Multiply both sides by 5v+6
So we have an intercept on the v-axis at
y-intercept (vertical axis intercept)
To find possible y-intercepts, evaluate
So we have an intercept on the y-axis at
holes
There are no holes. Nothing can be factored or "canceled out."
vertical asymptote
Find what value of
The denominator of
VA at
horizontal asymptote
For this rational function, the degree of the numerator and denominator are the same. So the horizontal asymptote is the ratio of the leading coefficients.
Since
HA at
end behavior
Using a calculator, substituting big positive numbers into the formula shows that it is below the horizontal asymptote as
Substituting big negative numbers into the formula shows that it is above the horizontal asymptote as
behavior around vertical asymptote
Using a calculator, substituting numbers slightly less than (to the left of) the vertical asymptote into the formula shows that
substituting numbers slightly bigger than (to the right of) the vertical asymptote into the formula shows that