Question

the graph of a parent function is shown
which function belongs to the same function family as the graphed function?
a. $f(x) = \frac{1}{2x - 3}$
b. $f(x) = \frac{1}{3}\sqrt3{x + 9}$
c. $f(x) = 9x^3 + 2$
d. $f(x) = 9\log 2x$

Explanation:

Step1: Identify parent function type

The graph is symmetric about the origin, increasing everywhere, and has the shape of a cube root function $f(x)=\sqrt[3]{x}$.

Step2: Match to option family

• Option A: Rational function ($\frac{1}{2x-3}$), different family.
• Option B: Cube root function ($\frac{1}{3}\sqrt[3]{x+9}$), same family.
• Option C: Cubic polynomial ($9x^3+2$), different family.
• Option D: Logarithmic function ($9\log 2x$), different family.

Answer:

B. $f(x) = \frac{1}{3}\sqrt{x + 9}$