Transformations of Linear Functions

Front

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

Back

A vertical translation involves shifting the graph of a function up or down without changing its shape.

Front

How does the graph of f(x) = x change when it is transformed to g(x) = f(x) + 2?

Back

The graph of f(x) = x is shifted vertically up by 2 units.

Front

What does it mean for a graph to be translated horizontally?

Back

A horizontal translation shifts the graph left or right without altering its shape.

Front

If the function f(x) is transformed to g(x) = 3f(x), what transformation occurs?

Back

The graph of f(x) is vertically stretched by a factor of 3.

Front

What is the effect of a vertical compression on a graph?

Back

A vertical compression reduces the distance between points on the graph and the x-axis, making the graph flatter.

Front

Describe the transformation of the graph of f(x) = x when it is changed to g(x) = f(x - 4).

Back

The graph of f(x) = x is shifted horizontally to the right by 4 units.

Front

What does the term 'parent function' refer to?

Back

A parent function is the simplest form of a function in a family of functions, from which other functions are derived.

Front

How does the transformation g(x) = f(x) - 2 affect the graph of f?

Back

The graph of f is shifted vertically down by 2 units.

Front

What is the result of replacing f(x) with f(x) + k, where k is a positive constant?

Back

The graph of f is translated vertically up by k units.

Front

Explain the transformation represented by the equation y = (1/2)x + 11.

Back

This equation represents a vertical compression by a factor of 1/2 and a vertical shift up by 11 units.