Question

graph the exponential function.
$f(x) = \frac{1}{2}(2)^x$
plot five points on the graph of the function. then click on the graph - a - function button.

Explanation:

Step1: Choose x-values

Select x - values, e.g., \(x=-2, - 1,0,1,2\).

Step2: Calculate f(x) for x=-2

Substitute \(x = - 2\) into \(f(x)=\frac{1}{2}(2)^{x}\).
\(f(-2)=\frac{1}{2}(2)^{-2}=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8} = 0.125\). So the point is \((-2,0.125)\).

Step3: Calculate f(x) for x=-1

Substitute \(x=-1\) into \(f(x)\).
\(f(-1)=\frac{1}{2}(2)^{-1}=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}=0.25\). Point: \((-1,0.25)\).

Step4: Calculate f(x) for x = 0

Substitute \(x = 0\) into \(f(x)\).
\(f(0)=\frac{1}{2}(2)^{0}=\frac{1}{2}\times1=\frac{1}{2}=0.5\). Point: \((0,0.5)\).

Step5: Calculate f(x) for x = 1

Substitute \(x = 1\) into \(f(x)\).
\(f(1)=\frac{1}{2}(2)^{1}=\frac{1}{2}\times2 = 1\). Point: \((1,1)\).

Step6: Calculate f(x) for x = 2

Substitute \(x = 2\) into \(f(x)\).
\(f(2)=\frac{1}{2}(2)^{2}=\frac{1}{2}\times4=2\). Point: \((2,2)\).

Answer:

Five points are \((-2,0.125)\), \((-1,0.25)\), \((0,0.5)\), \((1,1)\), \((2,2)\) (plot these on the graph).