Transformation of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the position, size, or shape of the graph of the function.

Front

What does a vertical shift of a function mean?

Back

A vertical shift moves the graph of the function up or down without changing its shape.

Front

What is the effect of subtracting a constant from a function, e.g., f(x) - c?

Back

Subtracting a constant c from a function f(x) shifts the graph down by c units.

Front

What is the effect of adding a constant to a function, e.g., f(x) + c?

Back

Adding a constant c to a function f(x) shifts the graph up by c units.

Front

What does the transformation f(x + c) represent?

Back

The transformation f(x + c) shifts the graph of the function left by c units.

Front

What does the transformation f(x - c) represent?

Back

The transformation f(x - c) shifts the graph of the function right by c units.

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.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x^2.

Front

How do you find the vertex of the absolute value function y = |x - h| + k?

Back

The vertex of the function y = |x - h| + k is the point (h, k).

Front

What is the effect of a vertical stretch on a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.