Respuesta :
Answer:
The value 3 represents the vertical translation upwards of [tex]f(x)[/tex] to [tex]g(x)[/tex]
Step-by-step explanation:
The question is incomplete or missing data.
The correct question
What value represents the vertical translation from the graph of the parent function [tex]f(x) = x^2[/tex] to the graph of the function
[tex]g(x) = (x + 5)^2 + 3[/tex]?
Given functions:
Parent function
[tex]f(x) = x^2[/tex]
Translated function
[tex]g(x) = (x + 5)^2 + 3[/tex]
Translation rules
For horizontal shift
[tex]f(x)\rightarrow f(x+c)[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the left.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the right.
For vertical shift
[tex]f(x)\rightarrow f(x)+c[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the up.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the down.
From the functions given the translation rule can be given as:
[tex]f(x)\rightarrow f(x+5)+3[/tex]
[tex]g(x)=f(x+5)+3[/tex]
This shows the graph is shifted left by 5 units and upwards by 3 units.
Thus the value 3 represents the vertical translation of [tex]f(x)[/tex] to [tex]g(x)[/tex]
