Function Transformations

Front

What is a vertical stretch in function transformations?

Back

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

Front

What does the transformation g(x) = f(x + 3) represent?

Back

The graph of f(x) is shifted left by 3 units.

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, from which other functions can be derived.

Front

Identify the transformation from f(x) = x^2 to g(x) = x^2 - 5.

Back

The graph is shifted down 5 units.

Front

What does the transformation h(x) = f(x) + 2 indicate?

Back

The graph of f(x) is shifted up 2 units.

Front

What is a vertical compression in function transformations?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

Front

What does the transformation g(x) = 3f(x) represent?

Back

The graph of f(x) is vertically stretched by a factor of 3.

Front

What does the transformation p(x) = f(x - 4) indicate?

Back

The graph of f(x) is shifted right by 4 units.

Front

What is the effect of a negative sign in front of a function, such as g(x) = -f(x)?

Back

The graph of f(x) is reflected over the x-axis.

Front

What does the transformation g(x) = f(-x) indicate?

Back

The graph of f(x) is reflected over the y-axis.