Answer:
[tex]f(x)=|x+4|+2[/tex]
Step-by-step explanation:
The given absolute value function is
[tex]f(x)=|x|[/tex]
This is the base or the parent function.
The transformation [tex]f(x)=|x+b|+c[/tex] will shift the parent function b units to the left and c units up.
From the question, b=4 units and c=2 units.
The new equation is [tex]f(x)=|x+4|+2[/tex]
Answer: The equation of the new function is [tex]f(x)=|x+4|+2.[/tex]
Step-by-step explanation: We are given to find the equation of the new function if we apply the following changes to the absolute value parent function f(x)=lxl :
Shift 4 units left and Shift 2 units up.
We know that
if we shift the absolute value parent function f(x) = |x| to h units left and k units up, then the new equation will be
[tex]f(x)=|x+h|+k.[/tex]
Therefore, if the function is shifted 4 units left and 2 units up, then the equation of the new function will be
[tex]f(x)=|x+4|+2.[/tex]
Thus, the equation of the new function is [tex]f(x)=|x+4|+2.[/tex]
