Transformations of Functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, from which other functions in the same family are derived. Examples include linear functions (f(x) = x), quadratic functions (f(x) = x²), and square root functions (f(x) = √x).

Front

What transformation occurs when a function is reflected across the x-axis?

Back

When a function is reflected across the x-axis, the output values (y-values) are multiplied by -1. For example, the reflection of f(x) is -f(x).

Front

What does it mean to shift a function vertically?

Back

Shifting a function vertically means moving it up or down on the graph. Adding a constant to the function shifts it up, while subtracting a constant shifts it down. For example, f(x) + 3 shifts the graph of f(x) up by 3 units.

Front

What is the effect of shifting a function horizontally?

Back

Shifting a function horizontally means moving it left or right. Adding a constant inside the function shifts it left, while subtracting a constant shifts it right. For example, f(x - 2) shifts the graph of f(x) right by 2 units.

Front

What is the square root function?

Back

The square root function is defined as f(x) = √x, where the output is the non-negative square root of x. Its graph starts at the origin (0,0) and increases gradually.

Front

What is an exponential function?

Back

An exponential function is a function of the form f(x) = a⋅b^x, where a is a constant, b is a positive real number, and x is the exponent. The graph of an exponential function increases rapidly for b > 1.

Front

How do you identify a quadratic function?

Back

A quadratic function is identified by its standard form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. Its graph is a parabola.

Front

What is the transformation of f(x) = |x| when reflected across the x-axis?

Back

The transformation of f(x) = |x| when reflected across the x-axis is g(x) = -|x|.

Front

What does it mean to compress a function vertically?

Back

Compressing a function vertically means reducing the distance between points on the graph and the x-axis. This is done by multiplying the function by a factor between 0 and 1. For example, 0.5f(x) compresses the graph of f(x) vertically.

Front

What is the transformation of f(x) = √x when shifted down 2 units?

Back

The transformation of f(x) = √x when shifted down 2 units is g(x) = √x - 2.