Question

Which direction would the graph of y=|x-4|+3 open?

down
left
right
up

Answer 1

the absolute value function will always open to the positive direction. Because this is in the form y = |x|, it opens up. If it was in the form of x = |y|, it would open right, however it is not, so it opens up.

Therefore the solution is up.

Answer 2

Up

Explanation:

Let the parent function be y=|x|

Rule : f(x)→f(x-b)

So, the graph shifts right by b units

So, shift the parent graph by 4 units to right

So, using rule |x|→|x-4|

So, new function = |x-4|

Rule :f(x)→f(x)+b

So, the graph shifts up by b units

So, shift the obtained graph by 3 units up

So, |x-4|→|x-4|+3

Thus the direction of the graph of y=|x-4|+3 open is up

Hence Option D is correct.