Questions: Reciprocal Functions Find the vertical asymptote. y=(5x-15)/(x+3) x=[?]

Reciprocal Functions Find the vertical asymptote. y=(5x-15)/(x+3) x=[?]
Transcript text: Reciprocal Functions Find the vertical asymptote. \[ \begin{array}{l} y=\frac{5 x-15}{x+3} \\ x=[?] \end{array} \]
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Solution

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Solution Steps

Step 1: Identify the denominator

The vertical asymptote of a reciprocal function occurs where the denominator equals zero (since division by zero is undefined). For the function \( y = \frac{5x - 15}{x + 3} \), the denominator is \( x + 3 \).

Step 2: Set the denominator equal to zero

To find the vertical asymptote, solve for \( x \) when the denominator is zero: \[ x + 3 = 0 \]

Step 3: Solve for \( x \)

Subtract 3 from both sides of the equation: \[ x = -3 \] This is the vertical asymptote of the function.

Final Answer

\(\boxed{x = -3}\)

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