Transformations of Linear Functions

Front

What is a vertical translation of a graph?

Back

A vertical translation moves the graph up or down without changing its shape. For example, f(x) + k translates the graph of f(x) vertically by k units.

Front

What does it mean to shift a graph horizontally?

Back

A horizontal shift moves the graph left or right. For example, f(x - h) shifts the graph of f(x) to the right by h units, while f(x + h) shifts it to the left by h units.

Front

What is a reflection in the context of graph transformations?

Back

A reflection flips the graph over a specific axis. For example, reflecting over the x-axis changes f(x) to -f(x).

Front

How does a vertical stretch affect a graph?

Back

A vertical stretch increases the distance of points from the x-axis. For example, if f(x) is multiplied by a factor greater than 1, the graph is stretched vertically.

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x, which is a straight line through the origin with a slope of 1.

Front

What transformation occurs when f(x) is replaced with f(x) - k?

Back

This represents a vertical translation down by k units.

Front

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

Back

This represents a vertical translation of the parent function f(x) = x, shifted up 3 units.

Front

If f(x) = x is transformed to f(x) = x - 5, what is the transformation?

Back

The graph is shifted down 5 units.

Front

What is the effect of the transformation f(x) = 2x?

Back

This represents a vertical stretch of the parent function by a factor of 2.

Front

How does the transformation f(x) = x + 4 affect the graph?

Back

The graph is shifted vertically up by 4 units.