Question

vertical stretches and shrinks of exponential functions
what is the value of a for the exponential function in the graph represented in the form of $f(x)=a(b^x)$?
options: -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 \( x = 0 \), \( b^0=1 \) (by the property of exponents, any non - zero number to the power of 0 is 1). So \( f(0)=a(b^0)=a\times1 = a \).

Step3: Find the y - intercept from the graph

Looking at the graph, when \( x = 0 \) (the y - axis), the graph passes through the point \( (0, 3) \). This means that \( f(0)=3 \). Since \( f(0)=a \), we can conclude that \( a = 3 \).

Answer:

3