graph the exponential function.\n\n$f(x)=(\\frac{5}{8})^x$\n\nplot five points on the graph of the function…

Explanation:

Step1: Find value when $x = - 2$

Substitute $x=-2$ into $f(x)=\left(\frac{5}{8}\right)^{x}$, we get $f(-2)=\left(\frac{5}{8}\right)^{-2}=\left(\frac{8}{5}\right)^{2}=\frac{64}{25} = 2.56$. So the point is $(-2,2.56)$.

Step2: Find value when $x=-1$

Substitute $x = - 1$ into $f(x)=\left(\frac{5}{8}\right)^{x}$, we get $f(-1)=\left(\frac{5}{8}\right)^{-1}=\frac{8}{5}=1.6$. So the point is $(-1,1.6)$.

Step3: Find value when $x = 0$

Substitute $x = 0$ into $f(x)=\left(\frac{5}{8}\right)^{x}$, we get $f(0)=\left(\frac{5}{8}\right)^{0}=1$. So the point is $(0,1)$.

Step4: Find value when $x = 1$

Substitute $x = 1$ into $f(x)=\left(\frac{5}{8}\right)^{x}$, we get $f(1)=\frac{5}{8}=0.625$. So the point is $(1,0.625)$.

Step5: Find value when $x = 2$

Substitute $x = 2$ into $f(x)=\left(\frac{5}{8}\right)^{x}$, we get $f(2)=\left(\frac{5}{8}\right)^{2}=\frac{25}{64}\approx0.39$. So the point is $(2,0.39)$.

Answer:

The five points are $(-2,2.56),(-1,1.6),(0,1),(1,0.625),(2,0.39)$