Functions
Functions
Allen Star Batch
Grade 12

Question:

The graph of the function $f(x) = \frac{9x+7}{3x+12}$ is symmetric to the point:
$(-4, 3)$
$(-3, 4)$
$(3, 4)$
$(-3, -4)$

Step-by-Step Solution

Key Concept: A rational function $f(x) = \frac{ax+b}{cx+d}$ represents a rectangular hyperbola with center of symmetry at the point $\left(-\frac{d}{c}, \frac{a}{c}\right)$. For $f(x) = \frac{9x+7}{3x+12}$, the center is at $\left(-\frac{12}{3}, \frac{9}{3}\right) = (-4, 3)$.
The given graph can be rewritten as $(y-3)(x+4) = -\frac{29}{3}$, representing a rectangular hyperbola with center at $(-4, 3)$.
Correct Answer: 1

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