Identify the equations of the asymptotes.

June 10, 2026Mathematics

ScanSolve AI Answer

June 10, 2026

Answer

x=2

Step 1: Identify the equations of the asymptotes. The given function is $f(x) = \frac{p}{x-2} + 4$ . For a hyperbola in the form $y = \frac{k}{x-a} + b$ , the vertical asymptote is $x=a$ and the horizontal asymptote is $y=b$ . Comparing $f(x)$ to the general form, we have $a=2$ and $b=4$ . The equations of the asymptotes are $x=2$ and $y=4$ .

The equations of the asymptotes are $x=2$ and $y=4$ .

Vertical asymptote: $\boxed{x=2}$
Horizontal asymptote: $\boxed{y=4}$

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Quick Answer

The given function is f(x) = (p)/(x-2) + 4.
For a hyperbola in the form y = (k)/(x-a) + b, the vertical asymptote is x=a and the horizontal asymptote is y=b.
Comparing f(x) to the general form, we have a=2 and b=4.
The equations of the asymptotes are x=2 and y=4.

Asked on June 10, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on June 10, 2026

Step 1: Identify the equations of the asymptotes. The given function is f(x) = (p)/(x-2) + 4. For a hyperbola in the form y = (k)/(x-a) + b, the vertical asymptote is x=a and the horizontal asymptote is y=b. Comparing f(x) to the general form, we have a=2 and b=4. The equations of the asymptotes are x=2 and y=4. The equations of the asymptotes are x=2 and y=4. Vertical asymptote: x=2 Horizontal asymptote: y=4 Send me the next one 📸