Question

if the function h(x) is the horizontal reflection of the function f(x)=x³, which of the following tables can be the data sets for both f(x) and h(x)? (1 point) option a x f(x) x h(x) 0 0 0 0 1 1 -1 -1 2 8 -2 -8 option b x f(x) x h(x) 0 0 0 0 1 3 -1 3 2 6 -2 6 option c x f(x) x h(x) 0 0 0 0 1 1 -1 1 2 8 -2 8 option d x f(x) x h(x) 0 0 0 0 1 1 -1 1 2 4 -2 4

Explanation:

Step1: Recall horizontal - reflection rule

The horizontal reflection of a function \(y = f(x)\) is \(y=h(x)=f(-x)\). Given \(f(x)=x^{3}\), then \(h(x)=(-x)^{3}=-x^{3}\).

Step2: Check values for \(f(x)\) and \(h(x)\)

For \(x = 0\), \(f(0)=0^{3}=0\) and \(h(0)=(-0)^{3}=0\). For \(x = 1\), \(f(1)=1^{3}=1\) and \(h(1)=(-1)^{3}=-1\). For \(x = 2\), \(f(2)=2^{3}=8\) and \(h(2)=(-2)^{3}=-8\).

Answer:

A. Option A:

x	f(x)	x	h(x)
1	1	-1	-1
2	8	-2	-8