Questions: Write an equation for a rational function with: Vertical asymptotes at x=-2 and x=2 x intercepts at x=6 and x=-4 y intercept at 2

Write an equation for a rational function with: Vertical asymptotes at x=-2 and x=2 x intercepts at x=6 and x=-4 y intercept at 2
Transcript text: Write an equation for a rational function with: Vertical asymptotes at $x=-2$ and $x=2$ $x$ intercepts at $x=6$ and $x=-4$ $y$ intercept at 2 \[ y= \] $\square$
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Solution

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Solution Steps

Step 1: Construct the Denominator

The denominator is constructed based on the given vertical asymptotes: $(x + 2) * (x - 2)$.

Step 2: Construct the Numerator

The numerator is constructed based on the given x intercepts: $(x - 6) * (x + 4)$.

Step 3: Determine the Constant $k$

Given a y intercept of 2, substitute $x = 0$ into the equation and solve for $k$ using the y intercept value. This gives $k = 0.33$.

Final Answer:

The constructed rational function is $y = 0.33 \cdot \frac{(x - 6) * (x + 4)}{(x + 2) * (x - 2)}$, rounded to 2 decimal places.

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