Linear Transformations

Front

What is the linear parent function?

Back

The linear parent function is f(x) = x, which represents a straight line with a slope of 1 and a y-intercept of 0.

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x - 3)?

Back

g(x) is shifted right 3 units.

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x + 3)?

Back

g(x) is shifted left 3 units.

Front

What is a translation of a linear function?

Back

A translation of a linear function is a vertical shift of the graph up or down.

Front

What transformation occurs when f(x) = x is replaced with f(x) + 2?

Back

Vertical translation up by 2 units.

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x) + 3?

Back

g(x) is shifted up 3 units.

Front

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

Back

A vertical shift moves the graph of a function up or down without changing its shape.

Front

What is the effect of adding a constant to the function f(x)?

Back

Adding a constant to f(x) results in a vertical shift of the graph.

Front

What is the effect of subtracting a constant from the input of the function f(x)?

Back

Subtracting a constant from the input results in a horizontal shift of the graph.

Front

If g(x) = f(x - 2), what transformation occurs?

Back

g(x) is shifted right 2 units.