Question

ng horizontal translations
graph: $f(x) = 2^{x - 1}$
step 1: find the value of $x$ that makes the exponent zero by solving this equation: $x - 1 = 0$
$x = 1$
calculate the value of the function.
$f(1) = $
options: 0, 1, 4
(graph with x-axis from -2 to 2 and y-axis from 1 to 4, grid lines, and a check button)

Explanation:

Step1: Substitute x=1 into f(x)

We know \( f(x) = 2^{x - 1} \), and we need to find \( f(1) \). Substitute \( x = 1 \) into the function: \( f(1)=2^{1 - 1} \).

Step2: Simplify the exponent

Simplify the exponent \( 1 - 1 = 0 \), so the function becomes \( f(1)=2^{0} \).

Step3: Evaluate the exponential expression

Recall that any non - zero number to the power of 0 is 1, so \( 2^{0}=1 \).

Answer:

1