Question

The exponential function, f(x) = 2x, undergoes two transformations to g(x) = 5 • 2x – 3. How does the graph change? Select all that apply.
A. It is shifted right.
B. It is vertically compressed.
C. It is flipped over the x-axis.
D. It is shifted down.
E. It is vertically stretched.

Answer 1

Answer:

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.