draw a graph of $f(x) = \\frac{2x}{x + 3}$ by first placing the horizontal and vertical asymptotes, then…
draw a graph of $f(x) = \\frac{2x}{x + 3}$ by first placing the horizontal and vertical asymptotes, then plotting an additional point on the graph.
Answer
Explanation:
Step1: Find the vertical asymptote
Set the denominator to zero and solve for $x$. $$x + 3 = 0 \implies x = -3$$
Step2: Find the horizontal asymptote
Compare the degrees of the numerator and denominator. $$y = \frac{2}{1} = 2$$
Step3: Find an additional point
Evaluate the function at a convenient $x$ value, such as $x = 0$. $$f(0) = \frac{2(0)}{0 + 3} = 0$$
Step4: Identify the plotting components
The graph is a hyperbola with the following features. Vertical Asymptote: $x = -3$; Horizontal Asymptote: $y = 2$; Point: $(0, 0)$.
Answer:
Vertical Asymptote: $x = -3$ Horizontal Asymptote: $y = 2$ Additional Point: $(0, 0)$