Transformations of Linear Functions

Front

What is a vertical translation of a function?

Back

A vertical translation of a function occurs when the entire graph of the function is shifted up or down by a certain number of units.

Front

How does the equation y = f(x) + d affect the graph of f(x)?

Back

The graph of f(x) is shifted up 'd' units.

Front

What does the equation y = f(x + c) represent?

Back

The graph of f(x) is shifted left 'c' units if c is positive, and right 'c' units if c is negative.

Front

What is a reflection of a function?

Back

A reflection of a function occurs when the graph is flipped over a specific axis, such as the x-axis or y-axis.

Front

How does the equation y = -f(x) transform the graph of f(x)?

Back

The graph of f(x) is reflected over the x-axis.

Front

What does a vertical stretch of a function mean?

Back

A vertical stretch occurs when the graph of the function is pulled away from the x-axis, making it steeper.

Front

How does the equation y = af(x) affect the graph if 'a' is greater than 1?

Back

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

Front

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

Back

The graph of f(x) is shifted down 3 units.

Front

What is the effect of the equation y = f(x) + 2 on the graph of f(x)?

Back

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

Front

How does the equation y = -3f(x) + 5 transform the graph of f(x)?

Back

The graph is reflected over the x-axis, vertically stretched by a factor of 3, and shifted up 5 units.