Transformations of Functions: Writing Equations

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of the function, which can include shifting, reflecting, stretching, or compressing.

Front

How do you shift a function to the right?

Back

To shift a function f(x) to the right by 'h' units, replace x with (x - h) in the function's equation.

Front

What is the equation for shifting f(x)=x^2 two units to the right?

Back

The equation is (x - 2)^2.

Front

How do you shift a function down?

Back

To shift a function f(x) down by 'k' units, subtract 'k' from the function's equation.

Front

What is the equation for shifting f(x)=x^3 four units down?

Back

The equation is x^3 - 4.

Front

What does g(x) = (x - 1)^3 represent if f(x) = x^3?

Back

It represents the function f(x) shifted to the right by 1 unit.

Front

How do you shift the absolute value function f(x)=|x| to the right by 2 units?

Back

The equation becomes g(x) = |x - 2|.

Front

What is the effect of adding a constant outside the function?

Back

Adding a constant outside the function shifts the graph vertically. For example, g(x) = f(x) + k shifts the graph up by k units.

Front

What is the equation for shifting f(x)=|x| down by 2 units?

Back

The equation is g(x) = |x| - 2.

Front

What does the equation y = √(x - 5) + 4 represent?

Back

It represents the square root function shifted right by 5 units and up by 4 units.