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Consider the function [tex]f(x)=2^x[/tex] and the function [tex]g(x)[/tex].

[tex]g(x)=f(x)+4=2^x+4[/tex]

How will the graph of [tex]g(x)[/tex] differ from the graph of [tex]f(x)[/tex]?

A. The graph of [tex]g(x)[/tex] is the graph of [tex]f(x)[/tex] vertically compressed 4 units.
B. The graph of [tex]g(x)[/tex] is the graph of [tex]f(x)[/tex] shifted 4 units downward.
C. The graph of [tex]g(x)[/tex] is the graph of [tex]f(x)[/tex] vertically stretched 4 units.
D. The graph of [tex]g(x)[/tex] is the graph of [tex]f(x)[/tex] shifted 4 units upward.

Sagot :

GinnyAnsweridn
To determine how the graph of [tex]\( g(x) \)[/tex] differs from the graph of [tex]\( f(x) \)[/tex], let's examine the given functions:
[tex]\[ f(x) = 2^x \][/tex]
[tex]\[ g(x) = f(x) + 4 = 2^x + 4 \][/tex]

The function [tex]\( g(x) \)[/tex] takes the original function [tex]\( f(x) \)[/tex] and adds 4 to it. This addition is applied to the output of [tex]\( f(x) \)[/tex], meaning that for any input [tex]\( x \)[/tex], the output of [tex]\( g(x) \)[/tex] is 4 units greater than the output of [tex]\( f(x) \)[/tex].

This can be visualized as a vertical shift:
- Adding a constant to a function results in a vertical shift of the graph.
- In this case, [tex]\( f(x) \)[/tex] is shifted vertically by [tex]\( +4 \)[/tex].

Therefore, the graph of [tex]\( g(x) \)[/tex] is the graph of [tex]\( f(x) \)[/tex] shifted 4 units upward.

The correct answer is:
D. The graph of [tex]\( g(x) \)[/tex] is the graph of [tex]\( f(x) \)[/tex] shifted 4 units upward.
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