Question

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.
$$ f ( x ) = \frac { 2 x + 9 } { 4 x - 2 } $$
plot rational function
vertical asymptote horizontal asymptote
x - intercept y - intercept hole
click on a feature then drag it into place.

Explanation:

Step1: Find the vertical asymptote

Set the denominator equal to zero: $4x - 2=0$. Solve for $x$: $4x=2$, so $x = \frac{1}{2}$.

Step2: Find the horizontal asymptote

Since the degree of the numerator and denominator are the same (both degree 1), the horizontal asymptote is the ratio of the leading coefficients. The leading coefficient of the numerator is 2 and of the denominator is 4. So $y=\frac{2}{4}=\frac{1}{2}$.

Step3: Find the x - intercept

Set the numerator equal to zero: $2x+9 = 0$. Solve for $x$: $2x=-9$, so $x=-\frac{9}{2}$.

Step4: Find the y - intercept

Set $x = 0$ in the function: $f(0)=\frac{2(0)+9}{4(0)-2}=\frac{9}{-2}=-\frac{9}{2}$.

Answer:

Vertical Asymptote: $x=\frac{1}{2}$, Horizontal Asymptote: $y = \frac{1}{2}$, x - intercept: $(-\frac{9}{2},0)$, y - intercept: $(0,-\frac{9}{2})$