Parent Graph Transformations - graphing and writing equations

Front

What is a parent graph?

Back

A parent graph is the simplest form of a function, which serves as a base for transformations.

Front

What does a vertical shift of 'k' units mean in a function?

Back

A vertical shift of 'k' units means the graph moves up if k is positive and down if k is negative.

Front

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

Back

The graph of f(x) shifts vertically by k units.

Front

What does a horizontal shift of 'h' units mean in a function?

Back

A horizontal shift of 'h' units means the graph moves left if h is positive and right if h is negative.

Front

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

Back

The graph of f(x) shifts horizontally by h units.

Front

What is the effect of a reflection across the x-axis on a function?

Back

A reflection across the x-axis changes the sign of the output values, resulting in y = -f(x).

Front

What is the effect of a reflection across the y-axis on a function?

Back

A reflection across the y-axis changes the sign of the input values, resulting in y = f(-x).

Front

What does a vertical stretch by a factor of 'a' do to the graph of a function?

Back

A vertical stretch by a factor of 'a' multiplies the output values by 'a', making the graph taller.

Front

What does a horizontal compression by a factor of 'b' do to the graph of a function?

Back

A horizontal compression by a factor of 'b' multiplies the input values by '1/b', making the graph narrower.

Front

What is the general form of a cubic function?

Back

The general form of a cubic function is f(x) = ax^3 + bx^2 + cx + d.