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.
$f(x) = \frac{3x + 6}{4x - 17}$
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: $4x - 17 = 0 \Rightarrow x = \frac{17}{4} = 4.25$

Step2: Find horizontal asymptote

Degree of numerator = degree of denominator: $y = \frac{3}{4} = 0.75$

Step3: Find x-intercept

Set numerator to 0: $3x + 6 = 0 \Rightarrow x = -2$

Step4: Find y-intercept

Set $x=0$: $f(0) = \frac{6}{-17} \approx -0.35$

Step5: Check for hole

No common factors in numerator/denominator: No hole

Answer:

Vertical Asymptote: $x = 4.25$
Horizontal Asymptote: $y = 0.75$
x-intercept: $(-2, 0)$
y-intercept: $(0, -\frac{6}{17})$
Hole: None