How do you find the base of an exponential function graph?

To find the base of an exponential function from its graph, you essentially need to determine the value 'b' in the function f(x) = b^x. The reference video provides an example that illustrates how to identify the base. Here’s a breakdown of how to approach this:

Identifying the Base

1. Understand the General Form: Recall that the exponential function is generally represented as f(x) = b^x, where 'b' is the base.

2. Analyze the Graph: Look for a point on the graph where the x-coordinate is equal to 1. The corresponding y-coordinate at x=1 will directly give you the base of the function.

3. Example: In the reference, if f(x) = b^x and f(1) = 4, then 'b' (the base) is 4. Thus, the exponential function is f(x) = 4^x.

Practical Steps

Here's a summarized approach:

• Step 1: Locate the point on the graph where x = 1.
• Step 2: Identify the y-value at that point.
• Step 3: This y-value is the base of the exponential function.

In simpler terms, if the graph passes through the point (1, k), the base of the exponential function is 'k'. Therefore, the function is f(x) = k^x.