Radical Functions Test

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical, such as a square root, cube root, etc. The general form is f(x) = @@ oot{n}{x}@@ where n is the degree of the root.

Front

What is the domain of the function f(x) = @@ oot{2}{x}@@?

Back

The domain of f(x) = @@ oot{2}{x}@@ is all real numbers, since square roots are defined for all non-negative values.

Front

What is the range of the function f(x) = @@ oot{2}{x}@@?

Back

The range of f(x) = @@ oot{2}{x}@@ is all non-negative real numbers, as the output of a square root function cannot be negative.

Front

How do you solve the equation @@ oot{2}{x} = 3@@?

Back

To solve @@ oot{2}{x} = 3@@, square both sides to get x = 9.

Front

What is the graph of the function f(x) = @@ oot{2}{x}@@?

Back

The graph of f(x) = @@ oot{2}{x}@@ is a curve that starts at the origin (0,0) and increases gradually, approaching infinity as x increases.

Front

What does the symbol @@ oot{n}{x}@@ represent?

Back

The symbol @@ oot{n}{x}@@ represents the nth root of x, which is a value that, when raised to the power of n, gives x.

Front

What is the difference between a radical and a radicand?

Back

Front

How do you simplify @@ oot{2}{x^2}@@?

Back

@@ oot{2}{x^2} = x@@, assuming x is non-negative.

Front

What is the effect of adding a constant to a radical function, such as in f(x) = @@ oot{2}{x} + 3@@?

Back

Adding a constant shifts the graph of the function vertically. In this case, the graph shifts up by 3 units.

Front

What is the equation of the graph that shifts f(x) = @@ oot{2}{x}@@ down by 3 units?

Back

The equation is f(x) = @@ oot{2}{x} - 3@@.