Unit 13 - Linear Transformations

Front

What is the linear parent function?

Back

y = x

Front

If the linear function f(x) = x is transformed to g(x) = f(x) - 6, what type of transformation occurs?

Back

g(x) is shifted down 6 units.

Front

Describe the transformation from f(x) to g(x) if g(x) is a vertical translation 2 units up of f(x).

Back

The graph of g is a vertical translation 2 units up of the graph of f.

Front

What happens to the graph of f(x) if it is reflected over the x-axis?

Back

The graph of g is a reflection of the graph of f.

Front

If the graph of the parent function f(x) = x is shifted 7 units down, what is the new equation?

Back

f(x) = x - 7.

Front

What is a vertical translation in the context of linear transformations?

Back

A vertical translation moves the graph up or down without changing its shape.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, there is a corresponding point (x, -y).

Front

What is a horizontal translation in linear transformations?

Back

A horizontal translation moves the graph left or right without changing its shape.

Front

If g(x) = 2f(x), what type of transformation is applied to the graph of f(x)?

Back

The graph of f(x) is vertically stretched by a factor of 2.

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.