Question

question 6 (1 point)

what is the symmetry point, if any, of the graph of the rational function.

\\((0, 0)\\)

\\((3, 1)\\)

Explanation:

🆕 New Concept Discovered: Symmetry of Rational Functions
Where the vertical and horizontal asymptotes cross.

Step 1: Identify the asymptotes

A simple rational function of the form \( f(x) = \frac{a}{x-h} + k \) is symmetric about the intersection point of its vertical and horizontal asymptotes, which is the point \( (h, k) \).

Looking at the graph:

• The vertical asymptote (the vertical dashed red line) is at:

$$ x = -3 $$

• The horizontal asymptote (the horizontal dashed red line) is at:

$$ y = 1 $$

Step 2: Find the intersection point

The point of symmetry is the intersection of these two asymptotes:

$$ (x, y) = (-3, 1) $$

Answer:

\( (-3, 1) \)