Option A: It is vertically stretched
Option B: it is shifted down
Solution:
The exponential function [tex]f(x)=2^{x}[/tex]undergoes two transformations to [tex]g(x)=5 \cdot 2^{x}-3[/tex].
To determine how the graph changes:
Consider the given exponential function [tex]f(x)=2^{x}[/tex].
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.
