Attributes of Square Root Functions

Front

What is a square root function?

Back

A square root function is a function of the form f(x) = √(x), where the output is the non-negative square root of the input x.

Front

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

Back

The domain of f(x) = √(x) is x ≥ 0, meaning the function is defined for all non-negative values of x.

Front

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

Back

The range of f(x) = √(x) is y ≥ 0, meaning the output values are all non-negative.

Front

How do you find the inverse of a square root function?

Back

To find the inverse of a square root function, swap x and y, then solve for y. For example, for f(x) = √(x), the inverse is f^(-1)(x) = x^2.

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, never going below the x-axis.

Front

What is the effect of a vertical shift on the graph of a square root function?

Back

A vertical shift moves the graph up or down. For example, f(x) = √(x) + 2 shifts the graph up by 2 units.

Front

What is the effect of a horizontal shift on the graph of a square root function?

Back

A horizontal shift moves the graph left or right. For example, f(x) = √(x - 3) shifts the graph right by 3 units.

Front

What is the equation of the graph that opens downwards?

Back

The equation of a square root function that opens downwards can be written as f(x) = k - √(x - h), where (h, k) is the vertex.

Front

How do you solve the equation √(x) = a?

Back

To solve √(x) = a, square both sides to get x = a^2, ensuring a is non-negative.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse reflect over the line y = x, meaning if (a, b) is on the function, then (b, a) is on the inverse.