Let f(x) = |x|, where x can be any real number. write a formula for the function whose graph is the
transformation of the graph of f given by the instructions below.
d. a translation left 4 units

Hello!

we have the function f(x) = IxI, and we want to write the formula if the function where we have the graph of f(x) translated left by 4 units.

Let's think it:

the graph of f(x) is like a V, where the vertix is at x = 0, then a translation to the left by 4 units mean that now the vertix is at x = -4, then in the new function, we have g( x = -4) = f(0)

This means that now we have

y = g(x) = f( x + 4) = Ix+4I

Always when you want a translation left by N units for the graph of f(x), you need to do:

y = g(x) = f( x +N)

and if the translation is to the right:

y = h(x) = f(x - N)

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,