College Math Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

How does the graph of g(x) = |x - 2| differ from f(x) = |x|?

Back

The graph of g(x) = |x - 2| is the graph of f(x) = |x| shifted 2 units to the right.

Front

What effect does adding a constant outside the function have on its graph?

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 if k > 0 and down by k units if k < 0.

Front

What is the effect of the transformation g(x) = f(x - 3)?

Back

The transformation g(x) = f(x - 3) shifts the graph of f(x) to the right by 3 units.

Front

What is the effect of the transformation g(x) = f(x) + 3?

Back

The transformation g(x) = f(x) + 3 shifts the graph of f(x) upward by 3 units.

Front

What is the parent function of quadratic functions?

Back

The parent function of quadratic functions is f(x) = x².

Front

How does the graph of g(x) = (x + 2)² - 3 differ from f(x) = x²?

Back

The graph of g(x) = (x + 2)² - 3 is the graph of f(x) = x² shifted 2 units to the left and 3 units down.

Front

What is the effect of a negative sign in front of a function, such as g(x) = -f(x)?

Back

A negative sign in front of a function reflects the graph across the x-axis.

Front

What is the parent function of cubic functions?

Back

The parent function of cubic functions is f(x) = x³.