SOLUTION: beginning with f(x) = squareroot of x, find the function g(x) that shows f(x) shifted to the left 2 units, reflected about the x axis, and then shifted up 7 units?

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Question 443245: beginning with f(x) = squareroot of x, find the function g(x) that shows f(x)
shifted to the left 2 units, reflected about the x axis, and then shifted up
7 units?
Found 2 solutions by swincher4391, stanbon:
Answer by swincher4391(1107) (Show Source):
You can put this solution on YOUR website!

Here are some rules for translations:
If it's inside the parenthesis/root:
+ = left
- = right
If it's outside the parenthesis/root:
+ = up
- = down
Reflect about the x axis:
g(x) = -f(x)
Reflect about the y axis:
g(x) = f(-x)
Reflect about the origin:
g(x) = -f(-x)
So using these rules, we should be able to construct a g(x):
If we are shifting left, then we add the amount inside of the root.

In addition we are moving up 7, so
Finally, we are reflecting about the x axis so, , which when we solve for g(x) gives us
So we have
Here is a graph so you can see the new translation.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
beginning with f(x) = squareroot of x, find the function g(x) that shows f(x)
shifted to the left 2 units, reflected about the x axis, and then shifted up
7 units?
----
f(x) = sqrt(x)
shifted left 2 units gives
a(x) = sqrt(x+2)
---
reflected about x axis gives
b(x) = -sqrt(x+2)
---
shifted up 7 units gives:
F(x) = -sqrt(x+2)+7
===============================
Cheers,
Stan H.
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