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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