Question

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

g(x) = 5.2^x - 3. How does the graph change?

Answer 1

Option A: It is vertically stretched

Option B: it is shifted down

Solution:

The exponential function
`f(x)=2^(x)`undergoes two transformations to
`g(x)=5 \cdot 2^(x)-3`.

To determine how the graph changes:

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

Let y = f(x)

Vertically compressed or stretched:

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.

Hence option A and option B is the correct answer.