Function Transformations

Front

What is a vertical shift in function transformations?

Back

A vertical shift moves the graph of a function up or down without changing its shape. For example, if f(x) is shifted down by 3 units, the new function is f(x) - 3.

Front

What does a horizontal shift to the left by 'h' units look like in function notation?

Back

A horizontal shift to the left by 'h' units is represented as f(x + h).

Front

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

Back

A vertical stretch increases the distance of points from the x-axis. If f(x) is stretched by a factor of 'a', the new function is a*f(x).

Front

How does reflecting a function over the y-axis affect its equation?

Back

Reflecting a function over the y-axis changes the sign of the x variable in the function's equation. For example, f(x) becomes f(-x).

Front

What is the parent function of a quadratic function?

Back

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

Front

Describe the transformation represented by f(x) = f(x - 2).

Back

This represents a horizontal shift to the right by 2 units.

Front

What does a negative sign in front of a function indicate?

Back

A negative sign indicates a reflection over the x-axis. For example, -f(x) reflects the graph of f(x) across the x-axis.

Front

What is the parent function of an absolute value function?

Back

The parent function of an absolute value function is f(x) = |x|.

Front

How do you represent a vertical shift up by 'k' units in function notation?

Back

A vertical shift up by 'k' units is represented as f(x) + k.

Front

What is the effect of a horizontal compression on a function?

Back

A horizontal compression makes the graph of the function narrower. If f(x) is compressed by a factor of 'b', the new function is f(bx).