Linear Transformations and Parent Function

Front

What is the linear parent function?

Back

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

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x) - 6?

Back

The graph is shifted down 6 units.

Front

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

Back

The graph is vertically translated up by 2 units.

Front

How does the equation y=(x-3)+5 shift from the parent function?

Back

It shifts 3 units to the right and 5 units up.

Front

Is the function f(x) = 2x + 3 linear or non-linear?

Back

Linear.

Front

What transformation occurs when g(x) = f(x + 6)?

Back

The graph is shifted left 6 units.

Front

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

Back

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

Front

What does a horizontal translation do to the graph of a function?

Back

A horizontal translation moves the graph left or right.

Front

What is the effect of a negative sign in front of the function, such as in g(x) = -f(x)?

Back

It reflects the graph across the x-axis.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line, meaning it has a constant rate of change.