Questions: Sketch the graph of the function and check the graph with a graphing calculator. Before doing so, describe how the graph of the function can be obtained from the graph of a basic exponential function. f(x) = 2^(x+3) - 5 Describe how the graph of the function can be obtained from the graph of a basic exponential function. Start with the graph of y = 2^x. Shift it units. right 3 units and then shift it 5

Sketch the graph of the function and check the graph with a graphing calculator. Before doing so, describe how the graph of the function can be obtained from the graph of a basic exponential function.
f(x) = 2^(x+3) - 5

Describe how the graph of the function can be obtained from the graph of a basic exponential function.

Start with the graph of y = 2^x. Shift it units.
right 3 units and then shift it 5

Transcript text: Sketch the graph of the function and check the graph with a graphing calculator. Before doing so, describe how the graph of the function can be obtained from the graph of a basic exponential function. \[ f(x)=2^{x+3}-5 \] Describe how the graph of the function can be obtained from the graph of a basic exponential function. Start with the graph of $y=2^{x}$. Shift it units. $\square$ right 3 units and then shift it $\square$ 5

Solution

Solution Steps

Step 1: Analyze the given function

The given function f(x) = 2^x-3 - 5 is a transformation of the basic exponential function y = 2^x.

Step 2: Identify the transformations

The function f(x) has two transformations:

Horizontal shift: x-3 in the exponent indicates a horizontal shift to the right by 3 units.
Vertical shift: -5 outside the exponential term indicates a vertical shift downwards by 5 units.

Step 3: Describe the transformation

Start with the graph of y = 2^x. Shift the graph 3 units to the right, and then shift it 5 units down.