graph the exponential function.\n\n$f(x)=\frac{1}{2}(5)^{x}$\n\nplot five points on the graph of the…

Explanation:

Step1: Find the point when $x = - 2$

Substitute $x=-2$ into $f(x)=\frac{1}{2}(5)^{x}$, we get $f(-2)=\frac{1}{2}(5)^{-2}=\frac{1}{2}\times\frac{1}{25}=\frac{1}{50}=0.02$. So the point is $(-2,0.02)$.

Step2: Find the point when $x=-1$

Substitute $x = - 1$ into $f(x)=\frac{1}{2}(5)^{x}$, we get $f(-1)=\frac{1}{2}(5)^{-1}=\frac{1}{2}\times\frac{1}{5}=\frac{1}{10}=0.1$. So the point is $(-1,0.1)$.

Step3: Find the point when $x = 0$

Substitute $x = 0$ into $f(x)=\frac{1}{2}(5)^{x}$, we get $f(0)=\frac{1}{2}(5)^{0}=\frac{1}{2}\times1 = 0.5$. So the point is $(0,0.5)$.

Step4: Find the point when $x = 1$

Substitute $x = 1$ into $f(x)=\frac{1}{2}(5)^{x}$, we get $f(1)=\frac{1}{2}(5)^{1}=\frac{5}{2}=2.5$. So the point is $(1,2.5)$.

Step5: Find the point when $x = 2$

Substitute $x = 2$ into $f(x)=\frac{1}{2}(5)^{x}$, we get $f(2)=\frac{1}{2}(5)^{2}=\frac{1}{2}\times25 = 12.5$. So the point is $(2,12.5)$.

Answer:

The five points are $(-2,0.02),(-1,0.1),(0,0.5),(1,2.5),(2,12.5)$