xand1r
Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

A function is translated from [tex]$f(x)=2^x$[/tex] to [tex]$g(x)=2^{x-3}$[/tex]. What is the effect on [tex][tex]$f(x)$[/tex][/tex]?

A. [tex]$f(x)$[/tex] moves 3 units upward.
B. [tex]$f(x)$[/tex] moves 3 units to the left.
C. [tex][tex]$f(x)$[/tex][/tex] moves 3 units to the right.
D. [tex]$f(x)$[/tex] moves 3 units downward.

Sagot :

GinnyAnswer
To understand the effect on [tex]\( f(x) \)[/tex] when it is translated to form [tex]\( g(x) \)[/tex], let's analyze the transformation.

Given the functions:
[tex]\[ f(x) = 2^x \][/tex]
[tex]\[ g(x) = 2^{x-3} \][/tex]

The transformation involves changing the variable [tex]\( x \)[/tex] in [tex]\( f(x) \)[/tex] to [tex]\( x-3 \)[/tex] in [tex]\( g(x) \)[/tex].

Horizontal shifts in the graphs of functions can be analyzed as follows:
- Replacing [tex]\( x \)[/tex] with [tex]\( x + c \)[/tex] shifts the graph [tex]\( c \)[/tex] units to the left.
- Replacing [tex]\( x \)[/tex] with [tex]\( x - c \)[/tex] shifts the graph [tex]\( c \)[/tex] units to the right.

Here, [tex]\( x \)[/tex] has been replaced with [tex]\( x - 3 \)[/tex], meaning the graph of [tex]\( f(x) \)[/tex] is shifted to the right by 3 units.

Therefore, the effect on [tex]\( f(x) \)[/tex] is:
[tex]\( f(x) \)[/tex] moves 3 units to the right.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.