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?
Algebra.Com
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.
===============
RELATED QUESTIONS
3. The parabola f(x)=x2 is transformed as described. State the equation that would... (answered by MathLover1)
The graph of x-7
f(x) = − 1/2 (1/6)
+9 is shifted left 7 units,... (answered by MathLover1)
The graph of
f(x) = -1/2 (1/6)exponent is x-7
+9 is shifted left 7 units,... (answered by MathLover1)
Let f(x)= √x. Find g(x), the function that is f(x) shifted up 10 units and left 9... (answered by ikleyn)
The graph of f(x) = x^2 is reflected in the x axis, vertically stretched by a factor of... (answered by TimothyLamb)
Given the square root function f(x)=√x , write the equation of this function... (answered by stanbon)
The function f(x) =x^2 +5x -6 is shifted 4 units to the left to create g(x). What is... (answered by greenestamps)
Which of the following transformations changes f(x)=x^3 to g(x)=4(x+2)^3?
Answer one... (answered by ikleyn)
3. The parabola f(x)=x2 is transformed as described. State the equation that would... (answered by MathLover1)