Transformations of Graphs

Front

What is a transformation of a graph?

Back

A transformation of a graph is a change made to the graph of a function that alters its position, shape, or size without changing its fundamental nature.

Front

What does a vertical stretch of a graph do?

Back

A vertical stretch of a graph multiplies the output values (y-values) of the function by a factor greater than 1, making the graph taller.

Front

What is a horizontal translation of a graph?

Back

A horizontal translation shifts the graph left or right along the x-axis without changing its shape.

Front

How does a reflection transformation affect a graph?

Back

A reflection transformation flips the graph over a specified axis, such as the x-axis or y-axis.

Front

What is the effect of a vertical translation on a graph?

Back

A vertical translation shifts the graph up or down along the y-axis.

Front

What does the equation g(x) = 2f(x) represent in terms of transformations?

Back

The equation g(x) = 2f(x) represents a vertical stretch of the graph of f(x) by a factor of 2.

Front

What does the equation y = (x + 2)^2 represent in terms of transformations?

Back

The equation y = (x + 2)^2 represents a horizontal translation of the graph of y = x^2, shifting it 2 units to the left.

Front

What is the general form of a function that has been translated left 'h' units and up 'k' units?

Back

The general form is y = f(x + h) + k.

Front

What is the effect of the transformation y = |x + 4| + 7 on the graph of y = |x|?

Back

This transformation translates the graph of y = |x| left 4 units and up 7 units.

Front

What is the difference between a vertical stretch and a vertical compression?

Back

A vertical stretch occurs when the output values are multiplied by a factor greater than 1, while a vertical compression occurs when the output values are multiplied by a factor between 0 and 1.