The exponential function f (x) = 2 * undergoes two transformations to

g (x) = 3 • 2x + 5. How does the graph change? Select all that apply.

Option (d) and (e) is correct.

Graph is shifted down and vertically stretched

Step-by-step explanation:

Given : The exponential function f (x) = 2^x undergoes two transformations to g (x) = 5/cdot 2^x-3

We have to choose the how the graph changes.

Consider the given exponential function f (x) = 2^x.

Vertically compressed or stretched

For a graph y = f (x),

A vertically compression (stretched) of a graph is compressing the graph toward x - axis.

• if k > 1, then the graph y = k• f (x), the graph will be vertically stretched by multiplying each y coordinate by k.

• if 0 < k < 1 if 0 < k < 1, the graph is f (x) vertically shrunk (or compressed) by multiplying each of its y-coordinates by k.

• if k should be negative, the vertical stretch or shrink is followed by a reflection across the x-axis.

Here, k = 5

So the graph will be vertically stretched

Also, Adding 3 to the graph will move the graph 3 units down so, the graph is shifted down.

So, The graph is shifted down.