Can u help me write an equation for each translation of y=|x|? 6 units left

1 Answer
Aug 1, 2018

y = |x+6|

Explanation:

So we can think of the plot of y = |x|:
graph{|x| [-10, 10, -2, 12]}

We want this to shift six units left, so it has to look like
graph{|x+6| [-10, 10, -2, 12]}

So we see really easily that the corner that used to be at 0 is now at -6. Also, the value at 0 is now 6. We can't just do something like |x| + c, since that would move the function up. Instead, if we put a number in the absolute value, it might do what we want.

So let's imagine |x+c|. At x=0, we get |c|, so we know that c = pm 6. We can now easily see which is it by plugging in x=-6. That should give us 0, and only does that when c = 6. Therefore, we get
y = |x+6|
which is what I plotted in the second equation.

The way that I think of it is that you have to get to x = 0 more quickly, so you have to add things. The numbers start "looking ahead" relative their normal values, which is why it shifts left and not right despite adding a number.