Question

which graph represents a function with an initial value of \\(\frac{1}{2}\\)?

Explanation:

Step1: Understand Initial Value

The initial value of a function (for a function \( y = f(x) \)) is the value when \( x = 0 \), i.e., \( f(0) \). We need to find the graph where the \( y \)-intercept (when \( x = 0 \)) is \( \frac{1}{2}=0.5 \).

Step2: Check Each Graph's \( x = 0 \) Point

• First graph: \( (0, 0.2) \) (not \( 0.5 \))
• Second graph: \( (0, 0.8) \) (not \( 0.5 \))
• Third graph: \( (0, 0.5) \) (matches \( \frac{1}{2} \))
• Fourth graph: \( (0, 0.4) \) (not \( 0.5 \))

Answer:

The graph on the Right (the third graph from the left, showing \( (0, 0.5) \))