Question

what is the value of a for the exponential function in the graph represented in the form of f(x) = a(b^x)? -4 -3 3 4

Explanation:

Step1: Recall the form of exponential function

The exponential function is given by \( f(x) = a(b^x) \). To find \( a \), we can use the \( y \)-intercept of the graph. The \( y \)-intercept occurs when \( x = 0 \).

Step2: Substitute \( x = 0 \) into the function

When \( x = 0 \), any non - zero number raised to the power of 0 is 1, so \( b^0=1 \). Then the function \( f(x)=a(b^x) \) becomes \( f(0)=a\times b^0=a\times1 = a \).

Step3: Find the \( y \)-intercept from the graph

Looking at the graph, when \( x = 0 \), the \( y \)-value (the value of the function at \( x = 0 \)) is 3. Since \( f(0)=a \), this means \( a = 3 \).

Answer:

3 (corresponding to the option "3")