Question

the function h is defined by the following rule. h(x)=4^x find h(x) for each x-value in the table. x | h(x) -3 | □ -2 | □ -1 | □ 0 | □ 1 | □

Explanation:

Step1: Substitute \(x = - 3\) into \(h(x)=4^{x}\)

According to the rule \(a^{-n}=\frac{1}{a^{n}}\), when \(x=-3\), \(h(-3)=4^{-3}=\frac{1}{4^{3}}=\frac{1}{64}\)

Step2: Substitute \(x = - 2\) into \(h(x)=4^{x}\)

When \(x = - 2\), \(h(-2)=4^{-2}=\frac{1}{4^{2}}=\frac{1}{16}\)

Step3: Substitute \(x=-1\) into \(h(x)=4^{x}\)

When \(x=-1\), \(h(-1)=4^{-1}=\frac{1}{4}\)

Step4: Substitute \(x = 0\) into \(h(x)=4^{x}\)

According to the rule \(a^{0}=1(a
eq0)\), when \(x = 0\), \(h(0)=4^{0}=1\)

Step5: Substitute \(x = 1\) into \(h(x)=4^{x}\)

When \(x = 1\), \(h(1)=4^{1}=4\)

Answer:

\(x\)	\(h(x)\)
\(-2\)	\(\frac{1}{16}\)
\(-1\)	\(\frac{1}{4}\)
\(0\)	\(1\)
\(1\)	\(4\)