Question

plot all of the existing five features of the following rational function (some may not be needed). if you get a fraction or decimal then plot as close to the true location as possible.
$f(x) = \frac{-4x}{3x + 7}$
plot rational function
vertical asymptote horizontal asymptote
x-intercept y-intercept hole
click on a feature then drag it into place.

Explanation:

Step1: Find vertical asymptote

Set denominator to 0: $3x + 7 = 0 \Rightarrow x = -\frac{7}{3} \approx -2.33$

Step2: Find horizontal asymptote

Degrees equal: ratio of leading coefficients $\frac{-4}{3} \approx -1.33$

Step3: Find x-intercept

Set numerator to 0: $-4x = 0 \Rightarrow x = 0$

Step4: Find y-intercept

Set $x=0$: $f(0) = \frac{0}{7} = 0$

Step5: Check for hole

No common factors in numerator/denominator: no hole

Answer:

Vertical Asymptote: $x = -\frac{7}{3}$
Horizontal Asymptote: $y = -\frac{4}{3}$
x-intercept: $(0, 0)$
y-intercept: $(0, 0)$
Hole: None