Radical Graphs

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) = √(x - h) + k, where (h, k) is the vertex.

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 increases gradually to the right, representing the positive square root of x.

Front

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

Back

The graph of f(x) = -√(x) is a reflection of f(x) = √(x) over the x-axis, resulting in a downward-opening curve.

Front

What effect does the transformation 'k' have in f(x) = √(x) + k?

Back

The transformation 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What does the transformation 'h' do in f(x) = √(x - h)?

Back

The transformation 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What is the vertex of the function f(x) = √(x - 4) - 2?

Back

The vertex of the function f(x) = √(x - 4) - 2 is at the point (4, -2).

Front

How do you identify a vertical stretch in a radical function?

Back

A vertical stretch occurs when the function is multiplied by a factor greater than 1, such as f(x) = a√(x) where a > 1.

Front

What is the effect of a vertical compression on a radical function?

Back

A vertical compression occurs when the function is multiplied by a factor between 0 and 1, such as f(x) = a√(x) where 0 < a < 1.

Front

What does a reflection over the x-axis do to the graph of a function?

Back

A reflection over the x-axis flips the graph upside down, changing the sign of the output values.

Front

What is the transformation for the function g(x) = -√(x - 4)?

Back

The function g(x) = -√(x - 4) is a reflection of f(x) = √(x - 4) over the x-axis.