Radical Functions

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.). The general form is @@f(x) = oot[n]{g(x)}@@ where g(x) is a polynomial.

Front

How does the graph of @@y = oot{(x)}@@ behave?

Back

The graph of @@y = oot{(x)}@@ is a half-parabola that opens to the right, starting at the origin (0,0) and increasing as x increases.

Front

What effect does the transformation @@y = oot{(x - h)}@@ have on the graph?

Back

The transformation shifts the graph of the radical function horizontally to the right by h units if h > 0, and to the left if h < 0.

Front

What effect does the transformation @@y = oot{(x)} + k@@ have on the graph?

Back

The transformation shifts the graph vertically. If k > 0, the graph shifts up by k units; if k < 0, it shifts down by k units.

Front

What does the negative sign in front of a radical function indicate?

Back

A negative sign in front of a radical function, such as @@y = - oot{(x)}@@, reflects the graph over the x-axis.

Front

How do you determine the domain of a radical function?

Back

Front

What is the range of the function @@y = oot{(x)}@@?

Back

Front

How do you find the x-intercept of a radical function?

Back

Front

What is the effect of adding a constant outside the radical, such as in @@y = oot{(x)} + 2@@?

Back

Adding a constant outside the radical shifts the graph vertically. In this case, the graph shifts up by 2 units.

Front

What is the effect of subtracting a constant outside the radical, such as in @@y = oot{(x)} - 3@@?

Back

Subtracting a constant outside the radical shifts the graph vertically down. In this case, the graph shifts down by 3 units.