Vertical Stretches and Shrinks of Exponential Functions Pre-Test Active 1 diri $3 \quad 4$ TIME REMAINING Which graph represents a function with an initial value of $\frac{1}{2} ?$ Mark this and return

Step 1 ：Find a function f(x) such that f(0) = \(\frac{1}{2}\)

Step 2 ：Use the exponential function form: f(x) = a * b^x

Step 3 ：Find the value of a when x = 0: f(0) = a * b^0

Step 4 ：Since b^0 = 1, we have f(0) = a

Step 5 ：Set f(0) = \(\frac{1}{2}\) and solve for a: a = \(\frac{1}{2}\)

Step 6 ：Replace a in the function: f(x) = \(\frac{1}{2}\) * b^x

Step 7 ：\(\boxed{f(x) = \frac{1}{2} * b^x}\), where b is any positive number different from 1