Question

Determine whether the graph below is that of a function by using the vertical line test if it is, use the graph to find
a) the domain an range
b) the intercepts, if any
c) any symmetry with respect to the x-axis, y-axis, or the origin.

Answer 1

This is the graph. I tried my best to draw it out. ;x

Answer 2

so first off we're looking at absolute value... You say the vertex is (6,-4) which means from the origin (0,0) it moved to the right 6 units and down 4 .. a) domain and range... let me ask you, if you look at the graph .. what values can x be ... and what values can y be?

Answer 3

I have no clue??? This graph is confusing to me.

Answer 4

I tried plugging it in with mathway and it didn't detect

Answer 5

okay... the arrows point both towards the left and right showing no indication of stopping, so it's (-infinity, +infinity) for your x's or domain.

Answer 6

Ok

Answer 7

What about the range and symmety?

Answer 8

see the -4 ... well if you look along the y-axis .. it doesn't go lower than -4 .. and then it will go infinity positive.. the range is (
-4,+infinity)

Answer 9

Ohhhhh ok gotcha so there is no symmetry

Answer 10

And the intercepts are what is given? (6,-4)

Answer 11

yeah the symmetry is at x=6 ... if I drew a line thru the x-axis at 6 .. the two lines would reflect

Answer 12

Ok Ok awesome got it

Answer 13

Wait so f+g(x)=7/4?

Answer 14

Never mind wrong one

Answer 15

it doesn't reflect over the y or x axis... oh did you get the intercepts figured out?

Answer 16

I thought the intercepts were 6,-4?

Answer 17

(6,-4) that's the vertex. The intercepts are where the line crosses at the axis. So the it's the point on the axis.. When x is zero then you have the yintercept. (0,?) When y is zero you have the x intercept. (?,0) but in this graph you have two x intercepts