Review 10: Shifting Linear Functions

Front

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

Back

A vertical translation occurs when a function is shifted up or down on the graph without changing its shape.

Front

If f(x) = x and g(x) = x + 3, what transformation has occurred?

Back

The graph of f has been vertically translated up by 3 units.

Front

What does it mean to shift a graph horizontally?

Back

Shifting a graph horizontally means moving it left or right along the x-axis.

Front

How does the equation y = x - 5 transform the parent function y = x?

Back

It shifts the graph of y = x down by 5 units.

Front

What is the effect of adding a positive constant to a function?

Back

Adding a positive constant results in a vertical shift upwards.

Front

What transformation occurs when the function is g(x) = x - 2?

Back

The graph of f(x) = x is shifted down 2 units.

Front

If g(x) = 2x, how does this transformation affect the graph of f(x) = x?

Back

The graph is vertically stretched by a factor of 2.

Front

What does a negative sign in front of a function indicate?

Back

A negative sign indicates a reflection across the x-axis.

Front

How does the function y = 3x + 1 differ from y = x?

Back

The graph of y = 3x + 1 is steeper and shifted up by 1 unit compared to y = x.

Front

What is the transformation from f(x) = x to g(x) = x + 4?

Back

The graph of f is shifted vertically up by 4 units.