Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does f(x + c) represent in function transformations?

Back

It represents a horizontal shift of the graph to the left by c units if c is positive, and to the right if c is negative.

Front

What does f(x) + k represent in function transformations?

Back

It represents a vertical shift of the graph upward by k units if k is positive, and downward if k is negative.

Front

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

Back

It reflects the graph of the function over the x-axis.

Front

What does a vertical stretch by a factor of a > 1 do to the graph of a function?

Back

It makes the graph taller and steeper, pulling points away from the x-axis.

Front

What does a vertical compression by a factor of 0 < a < 1 do to the graph of a function?

Back

It makes the graph shorter and flatter, pushing points closer to the x-axis.

Front

What is the parent function of f(x) = |x|?

Back

The parent function is the absolute value function, which creates a V-shaped graph.

Front

How does the graph of f(x) = 2|x| - 3 differ from its parent function?

Back

It is vertically stretched by a factor of 2 and shifted down 3 units.

Front

What is the transformation represented by f(x) = √(x - 5) + 4?

Back

The graph is shifted right 5 units and up 4 units from the parent function y = √x.

Front

What does the notation f(-x) indicate about the graph of a function?

Back

It indicates a reflection of the graph over the y-axis.