Question

graph: $f(x) = \frac{3}{2}(2)^x$
step 1: calculate the initial value of the function.
$f(0) = 1.5$
step 2: plot the initial value of the function at $(0, 1.5)$.
step 3: evaluate the function at two more points.
$f(1) = 3$ $f(-1) = $ dropdown with 0.75, 1, 3
(graph with y-axis from 1 to 4, x-axis from -2 to 2, point at (0,1.5))

Explanation:

Step1: Substitute \( x = -1 \) into \( f(x) \)

Given \( f(x) = \frac{3}{2}(2)^x \), substitute \( x = -1 \):
\( f(-1) = \frac{3}{2}(2)^{-1} \)

Step2: Simplify the expression

Recall that \( a^{-n} = \frac{1}{a^n} \), so \( (2)^{-1} = \frac{1}{2} \).
Then \( f(-1) = \frac{3}{2} \times \frac{1}{2} = \frac{3}{4} = 0.75 \).

Answer:

0.75