Questions: Graph the exponential function y=3^(x+2)

Transcript text: Graph the exponential function $y=3^{(x+2)}$

Solution

Solution Steps

Step 1: Identify the function

The given function is $y = 3^{(x + 2)}$ .

Step 2: Determine the transformation

The function $y = 3^{(x + 2)}$ is an exponential function with a base of 3. The $+2$ inside the exponent indicates a horizontal shift to the left by 2 units.

Step 3: Analyze the graph behavior

For the function $y = 3^{(x + 2)}$ :

As $x$ approaches negative infinity, $y$ approaches 0.
As $x$ increases, $y$ increases exponentially.

Final Answer

The correct graph is the first one, which shows an exponential growth starting from the left and increasing rapidly as $x$ increases.

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