Question

x | f(x)
-2 | 1/8
-1 | 1/4
0 | 1/2
1 | 1
2 | 2
what is the initial value of the exponential function represented by the table?
options: 1/8, 1/4, 1/2, 1

Explanation:

Step1: Recall the definition of initial value of an exponential function

The initial value of an exponential function \( f(x) = a(b)^x \) is the value of the function when \( x = 0 \), that is \( f(0) \). This is because when \( x = 0 \), \( b^0=1 \), so \( f(0)=a\times1 = a \), where \( a \) is the initial value.

Step2: Find the value of \( f(x) \) when \( x = 0 \) from the table

Looking at the given table, when \( x = 0 \), the corresponding value of \( f(x) \) is \( \frac{1}{2} \).

Answer:

C. \(\frac{1}{2}\) (assuming the options are labeled as A. \(\frac{1}{8}\), B. \(\frac{1}{4}\), C. \(\frac{1}{2}\), D. \(1\))