MATH SOLVE

4 months ago

Q:
# 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

A:

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.