Question

c) the function $f(x) = x^3$, which has been reflected across the $x$-axis, compressed vertically by a factor of $\frac{1}{2}$, and shifted up 2.

Explanation:

Step1: Reflect across x-axis

$g_1(x) = -x^3$

Step2: Vertically compress by $\frac{1}{2}$

$g_2(x) = \frac{1}{2}(-x^3) = -\frac{1}{2}x^3$

Step3: Shift up by 2 units

$g(x) = -\frac{1}{2}x^3 + 2$

Answer:

$g(x) = -\frac{1}{2}x^3 + 2$