Question

Describe the translations of the following function
Y = -1/3 |x + 4| - 2
can someone please help me :/

Answer 1

Hmm, well consider if the parent function is just \(\large y = |x|\)

That looks like

Answer 2

What happens when we add or subtract a number from JUST that x?? It shifts the graph over to the left or the right depending on adding or subtracting

So here

Gong from \(\large y = |x|\) to \(\large y = |x + 4|\) causes a shift to the LEFT 4 units

So now we have

Answer 3

Now, we see that a number is being subtracted from the whole function *not just the 'x'* so what THAT does is cause a VERTICAL translation...*down 2 units in this case

so

\(\large y = |x + 4|\) to \(\large y = |x + 4| - 2\) looks like