Question

a horizontal translation of 3 to the left is performed on the equation ( y = |x| + 1 ). what equation shows the graph of the outcome?
( \bigcirc y = |x + 3| + 1 )
( \bigcirc y = |x| + 3 )
( \bigcirc y = |x - 3| + 1 )
( \bigcirc y = |x| - 3 )

Explanation:

Step1: Recall horizontal shift rule

For $y=f(x)$, left shift $h$ units: $y=f(x+h)$

Step2: Apply shift to given function

Original: $y=|x|+1$. Shift left 3: $y=|x+3|+1$

Answer:

$y=|x+3|+1$