Transformation & Solving of Square Root Functions

Front

What is the equation of the graph for the function that has been transformed to the right by 5 and up by 4?

Back

y = \sqrt{x - 5} + 4

Front

Describe the transformation of the function f(x) = \sqrt{x + 2} - 4.

Back

Translate Left 2, Down 4

Front

What is the equation of the graph for the function that is reflected over the x-axis and shifted up by 3?

Back

y = -\sqrt{x} + 3

Front

What transformations occur in the function f(x) = -2\sqrt{x - 5} compared to the parent function?

Back

Reflected over the x-axis, vertical stretch by 2, and shifted right 5

Front

What transformations are applied to the function f(x) = -\sqrt{x} - 2?

Back

Reflect over x-axis, Down 2

Front

What is the parent function of square root functions?

Back

f(x) = \sqrt{x}

Front

How does the graph of f(x) = \sqrt{x} + 3 differ from the parent function?

Back

It is shifted up by 3.

Front

What effect does the negative sign in front of the square root function have?

Back

It reflects the graph over the x-axis.

Front

If f(x) = \sqrt{x - 4}, what transformation has occurred compared to the parent function?

Back

Shifted right 4.

Front

What is the effect of adding a constant outside the square root function, such as in f(x) = \sqrt{x} + k?

Back

It shifts the graph vertically by k units.