Answer:
[tex]f(x) = |x| +1[/tex]
Step-by-step explanation:
It looks like [tex]f(x)[/tex] has a parent function that is the absolute value of [tex]x[/tex]. If we let that parent function to be [tex]g(x)[/tex], [tex]g(x) = |x|[/tex]. Notice for every [tex]g(x)[/tex], [tex]f(x)[/tex] is [tex]1[/tex] more than [tex]g(x)[/tex] like [tex]g(1) = 1[/tex], [tex]f(1) = g(1) +1 = 2[/tex].So, [tex]f(x) = g(x) +1[/tex].
Solving for [tex]f(x)[/tex]:
[tex]f(x) = g(x) +1 \\ f(x) = |x| +1[/tex]
