Square Root Functions Review

Front

What is a square root function?

Back

A square root function is a function of the form f(x) = √(x), which represents the principal square root of x.

Front

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

Back

The domain of f(x) = √(x) is [0, ∞) because the square root is defined for non-negative values.

Front

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

Back

The range of f(x) = √(x) is [0, ∞) because the output of the square root function is always non-negative.

Front

Describe the transformation of f(x) = √(x) to g(x) = √(x) + 3.

Back

The graph of g(x) is the graph of f(x) shifted up by 3 units.

Front

What does it mean to reflect a function over the x-axis?

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is the effect of a vertical stretch by a factor of 2 on the function f(x) = √(x)?

Back

The new function will be g(x) = 2√(x), which makes the graph steeper.

Front

How do you find the initial point of the function f(x) = √(x - 1) - 3?

Back

Set the inside of the square root to zero: x - 1 = 0, so x = 1. The initial point is (1, -3).

Front

What is the range of the function f(x) = -√(x + 4) - 1?

Back

The range is (-∞, -1] because the maximum value of the function is -1 when x = -4.

Front

What transformation occurs when you replace f(x) with -f(x)?

Back

This transformation reflects the graph of the function over the x-axis.

Front

What does the notation f(x) = -3√(x - 2) + 1 indicate about the graph?

Back

This indicates a reflection over the x-axis, a vertical stretch by a factor of 3, a right shift by 2 units, and an upward shift by 1 unit.