Transforming Parent Functions

Front

What is a parent function?

Back

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

Front

What transformation does g(x) = f(x - 1) - 5 represent?

Back

f(x) has been translated to the right one and down five.

Front

What transformation does p(x) = f(x + 3) represent?

Back

f(x) has been translated to the left three units.

Front

What is the effect of adding a constant to a function, such as in h(x) = f(x) + 2?

Back

It translates the function vertically; in this case, it moves the graph up 2 units.

Front

What is the effect of subtracting a constant from a function, such as in g(x) = f(x) - 5?

Back

It translates the function vertically; in this case, it moves the graph down 5 units.

Front

What transformation does g(x) = (x - 5)^2 represent?

Back

It translates the function horizontally to the right by 5 units.

Front

What transformation does g(x) = (x + 5)^2 represent?

Back

It translates the function horizontally to the left by 5 units.

Front

What is the equation of the parent function for quadratic functions?

Back

f(x) = x^2.

Front

What is the equation of the parent function for cubic functions?

Back

f(x) = x^3.

Front

What is the equation of the parent function for absolute value functions?

Back

f(x) = |x|.