Graphing Radicals

Front

What is the general form of a radical function?

Back

A radical function is a function that contains a variable within a radical (root) symbol, typically expressed as f(x) = √(g(x)) or f(x) = ∛(g(x)).

Front

What does the graph of f(x) = √x look like?

Back

The graph of f(x) = √x is a curve that starts at the origin (0,0) and rises to the right, becoming less steep as x increases.

Front

How does the graph of f(x) = √(x - 3) transform the graph of f(x) = √x?

Back

The graph of f(x) = √(x - 3) is shifted 3 units to the right.

Front

What is the effect of a negative sign in front of a radical function, such as f(x) = -√x?

Back

A negative sign reflects the graph of the function across the x-axis.

Front

Describe the transformation of f(x) = √x + 2 compared to f(x) = √x.

Back

The graph of f(x) = √x + 2 is shifted 2 units upward.

Front

What does the notation f(x) = ∛(x) represent?

Back

It represents the cube root function, which gives the cube root of x.

Front

How do you identify the transformations in the function f(x) = -∛(x + 3) - 1?

Back

This function is reflected across the x-axis, shifted 3 units to the left, and 1 unit down.

Front

What is the domain of the function f(x) = √(x - 4)?

Back

The domain is x ≥ 4, as the expression under the square root must be non-negative.

Front

What is the range of the function f(x) = -√x?

Back

The range is all real numbers less than or equal to 0, as the function outputs negative values.

Front

How does the graph of f(x) = ∛x differ from f(x) = √x?

Back

The graph of f(x) = ∛x is defined for all real numbers and has a point of inflection at (0,0), while f(x) = √x is only defined for non-negative x.