1. ## Transformation

The graph of F(X)= X^(1/2), shift down 3 and then reflect off the x-axis

I'm getting F(X)=-1(x)^(1/2)-3, but the answer in the book has F(x)= -1(x)^(1/2)+3

When I reflect my y values do I also reflect my shift?

2. Originally Posted by Crazyheaven
The graph of F(X)= X^(1/2), shift down 3 and then reflect off the x-axis

I'm getting F(X)=-1(x)^(1/2)-3, but the answer in the book has F(x)= -1(x)^(1/2)+3

When I reflect my y values do I also reflect my shift?
If g is obtained by reflection of f over the x-axis, $\displaystyle g(x) = (-1) \cdot f(x)$

$\displaystyle f(x)=x^{\frac12}$ ........ Original function

$\displaystyle f(x)=x^{\frac12} - 3$ ........ Translation by three units down

$\displaystyle f(x)=(-1) \cdot \left(x^{\frac12}-3\right)$ ........ Reflection over the x-axis

Thus $\displaystyle f(x)=-x^{\frac12} + 3$

3. Originally Posted by earboth
If g is obtained by reflection of f over the x-axis, $\displaystyle g(x) = (-1) \cdot f(x)$

$\displaystyle f(x)=x^{\frac12}$ ........ Original function
$\displaystyle f(x)=x^{\frac12} - 3$ ........ Translation by three units down
$\displaystyle f(x)=(-1) \cdot \left(x^{\frac12}-3\right)$ ........ Reflection over the x-axis
Thus $\displaystyle f(x)=-x^{\frac12} + 3$