Question

Question was provided via image upload.

Explanation:

Identify the function and points

The image shows an interactive exploration titled "Explore the Graph of a Basic Exponential Function".
The text states: "The graph of the function \(f(x) = 2^x\) is shown. Click each point for an explanation of where the point comes from."
The prompt box instructs: "Click the point \((0, 1)\) to begin your exploration."

Let us evaluate the function \(f(x) = 2^x\) at the integer values of \(x\) shown on the graph to find the coordinates of the plotted points:

• For \(x = -3\): \(f(-3) = 2^{-3} = \frac{1}{8} = 0.125\)
• For \(x = -2\): \(f(-2) = 2^{-2} = \frac{1}{4} = 0.25\)
• For \(x = -1\): \(f(-1) = 2^{-1} = \frac{1}{2} = 0.5\)
• For \(x = 0\): \(f(0) = 2^0 = 1\)
• For \(x = 1\): \(f(1) = 2^1 = 2\)
• For \(x = 2\): \(f(2) = 2^2 = 4\)
• For \(x = 3\): \(f(3) = 2^3 = 8\)

Determine the coordinates of the starting point

The prompt specifically asks to click the point \((0, 1)\) to begin the exploration.
This point corresponds to the \(y\)-intercept of the exponential function \(f(x) = 2^x\), where \(x = 0\) and \(y = 2^0 = 1\).

Answer:

The graph represents the basic exponential function:

$$f(x) = 2^x$$

To begin the exploration as instructed, locate and select the point:

$$(0, 1)$$