graph the given function by making a table of coordinates.\n\n f(x)=left(\frac{3}{4}\right)^{x} \n\ncomplete…

Explanation:

Step1: Substitute (x = - 2) into (f(x)=\left(\frac{3}{4}\right)^{x})

Use the rule (a^{-n}=\frac{1}{a^{n}}), so (y = f(-2)=\left(\frac{3}{4}\right)^{-2}=\frac{1}{\left(\frac{3}{4}\right)^{2}}=\frac{16}{9})

Step2: Substitute (x=-1) into (f(x)=\left(\frac{3}{4}\right)^{x})

Using (a^{-n}=\frac{1}{a^{n}}), we get (y = f(-1)=\left(\frac{3}{4}\right)^{-1}=\frac{4}{3})

Step3: Substitute (x = 0) into (f(x)=\left(\frac{3}{4}\right)^{x})

By the rule (a^{0}=1(a\neq0)), then (y = f(0)=\left(\frac{3}{4}\right)^{0}=1)

Step4: Substitute (x = 1) into (f(x)=\left(\frac{3}{4}\right)^{x})

Direct substitution gives (y = f(1)=\frac{3}{4})

Step5: Substitute (x = 2) into (f(x)=\left(\frac{3}{4}\right)^{x})

(y = f(2)=\left(\frac{3}{4}\right)^{2}=\frac{9}{16})

Answer:

When (x=-2), (y = \frac{16}{9}); when (x=-1), (y=\frac{4}{3}); when (x = 0), (y = 1); when (x=1), (y=\frac{3}{4}); when (x = 2), (y=\frac{9}{16})