Hi!

I can tell the domain from the graph of these functions but how do I tell the range from their graphs?

and

I can find the domain easily:

Also, why does the graph of flip over thex-axisand the graph of flip over they-axis?

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- Apr 28th 2013, 05:51 PMUnrealGraphing square root functions
Hi!

I can tell the domain from the graph of these functions but how do I tell the range from their graphs?

and

I can find the domain easily:

Also, why does the graph of flip over the**x-axis**and the graph of flip over the**y-axis**? - Apr 28th 2013, 06:01 PMProve ItRe: Graphing square root functions
Think about the transformations to a function f(x). -f(x) is a reflection over the x-axis while f(-x) is a reflection over the y-axis.

As for working out the range, for a standard function , the range is . Why? Now what transformations have been applied and how does this affect the range? - Apr 28th 2013, 06:14 PMUnrealRe: Graphing square root functions
- Apr 28th 2013, 06:23 PMProve ItRe: Graphing square root functions
No, I meant you start with the square root function and then apply some transformations to get the functions you have been given. What are these transformations?

- Apr 28th 2013, 06:39 PMUnrealRe: Graphing square root functions
- Apr 28th 2013, 06:42 PMProve ItRe: Graphing square root functions
Correct, so now what are the ranges of these functions?

- Apr 28th 2013, 06:52 PMUnrealRe: Graphing square root functions
Range refers to y-values.

Range:

Range: - Apr 28th 2013, 06:57 PMProve ItRe: Graphing square root functions
I agree with your range for f(x) but not your range for h(x).

- Apr 28th 2013, 07:11 PMUnrealRe: Graphing square root functions
- Apr 28th 2013, 07:20 PMProve ItRe: Graphing square root functions
This is correct. And I don't think it's counter-intuitive at all actually, it should be obvious that when there's a reflection in one of the axes then either the domain or range will be inverted.