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

Explanation:

Step1: Choose values for x

Select five distinct values for the independent variable $x$. Let's choose $x = -2, -1, 0, 1, 2$.

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

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

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

Substitute $x = -1$ into the function. $f(-1) = -\frac{1}{2}(2)^{-1} = -\frac{1}{2} \times \frac{1}{2^1} = -\frac{1}{2} \times \frac{1}{2} = -\frac{1}{4}$ The point is $(-1, -\frac{1}{4})$.

Step4: Calculate f(x) for x = 0

Substitute $x = 0$ into the function. $f(0) = -\frac{1}{2}(2)^0 = -\frac{1}{2} \times 1 = -\frac{1}{2}$ The point is $(0, -\frac{1}{2})$.

Step5: Calculate f(x) for x = 1

Substitute $x = 1$ into the function. $f(1) = -\frac{1}{2}(2)^1 = -\frac{1}{2} \times 2 = -1$ The point is $(1, -1)$.

Step6: Calculate f(x) for x = 2

Substitute $x = 2$ into the function. $f(2) = -\frac{1}{2}(2)^2 = -\frac{1}{2} \times 4 = -2$ The point is $(2, -2)$.

Answer:

Five points on the graph of the function $f(x) = -\frac{1}{2}(2)^x$ are: $(-2, -0.125)$ $(-1, -0.25)$ $(0, -0.5)$ $(1, -1)$ $(2, -2)$

To graph the function, plot these five points on the coordinate plane and draw a smooth curve passing through them. The graph will be an exponential decay curve reflected across the x-axis, approaching the x-axis as $x \to -\infty$ and decreasing rapidly as $x \to \infty$.