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.

Accepted Solution

Answer: Option (d) and (e) is correct. Graph is shifted down and vertically stretched  Step-by-step explanation: Given : The exponential function [tex]f(x)=2^x[/tex] undergoes two transformations to [tex]g(x)=5\cdot 2^x-3[/tex] We have to choose the how the graph changes. Consider the given exponential function [tex]f(x)=2^x[/tex]. 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.