Question

what is the initial value of the exponential function shown on the graph? 0 2 1 4

Explanation:

Step1: Recall initial value definition

The initial value of an exponential function \( y = ab^x \) is the value when \( x = 0 \), i.e., \( y(0)=a \). So we need to find the \( y \)-intercept (where \( x = 0 \)) of the exponential graph.

Step2: Identify the \( y \)-intercept from the graph

Looking at the graph, when \( x = 0 \) (the \( y \)-axis), the graph intersects the \( y \)-axis at \( y = 4 \). So the initial value (the value when \( x = 0 \)) is 4.

Answer:

4 (corresponding to the option with value 4)