determine whether the graph represents a function and then determine the domain and range of the function. graph is showing points at (-9,4) and (9,4) with the middle of the U at (0,-5)

Question

anonymous · Answer

attachment

anonymous · Answer

@whpalmer4

whpalmer4 · Answer

Function test:  can you draw a vertical line at any point that crosses the curve more than once?  If so, it's not a function.  A function will have one and only 1 y-value for each x-value, which obviously isn't true if you can connect two points on the curve with a vertical line.

anonymous · Answer

I figured that it wasnt a function but I dont know what the domain and range would be

anonymous · Answer

I was think that the domain would be -9 and 9 and the range be 4 and 4

whpalmer4 · Answer

Oh, but it is a function...for each x value, there's only 1 y value, right?  Is there any value of x for which the curve has two y values?

whpalmer4 · Answer

If you turned the diagram 90 degrees in either direction, so that it opened to the right or the left, that would be an example of a relationship that is not a function.

anonymous · Answer

oh ok I see what you mean yeah there is only 1

whpalmer4 · Answer

Domain would be -9 through 9 or $-9 \le x \le 9$ — the endpoints are included.  The range is the minimum value of the function through the maximum value of the function.

anonymous · Answer

4 ≤y≤-5?

anonymous · Answer

is that correct

whpalmer4 · Answer

Hmm, you want all the values that are greater than or equal to 4 and yet are also less than or equal to -5? :-)

whpalmer4 · Answer

In all my years, I can't say I've come across any that meet those constraints :-)

whpalmer4 · Answer

How would you say it in words?

anonymous · Answer

I have no idea

whpalmer4 · Answer

All the numbers between -5 and 4?

whpalmer4 · Answer

All the numbers that are greater than or equal to -5, and less than or equal to 4?

anonymous · Answer

it would be all the numbers that are greater than or equal to -5 and less than or equal to 4

anonymous · Answer

but I dont know how I would write that in a compound inequality

whpalmer4 · Answer

$$-5 \le y \le 4$$

anonymous · Answer

oh ok I just had it backwards

whpalmer4 · Answer

You sort of have to reverse the inequality sign on the left side from what you would say:
"all the numbers that are greater than or equal to -5" becomes "-5 is less than or equal to all the numbers"

anonymous · Answer

ok thanks once again