Parent functions and transformations 1st sem final review

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

Name the parent function for linear equations.

Back

The parent function for linear equations is f(x) = x.

Front

What is the parent function for quadratic equations?

Back

The parent function for quadratic equations is f(x) = x².

Front

What is the parent function for absolute value functions?

Back

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

Front

What is the parent function for cubic equations?

Back

The parent function for cubic equations is f(x) = x³.

Front

How does the graph of g(x) = x² - 5 relate to the parent function f(x) = x²?

Back

The graph of g(x) = x² - 5 is a vertical translation of the parent function f(x) = x², shifted down by 5 units.

Front

What transformation does the equation f(x) = -|x| - 1 represent?

Back

The equation f(x) = -|x| - 1 represents a reflection over the x-axis and a vertical shift down by 1 unit.

Front

What does the equation y = |x - 3| represent in terms of transformations?

Back

The equation y = |x - 3| represents a horizontal shift of the parent function |x| to the right by 3 units.

Front

Identify the transformation in g(x) = (x + 5)².

Back

The transformation in g(x) = (x + 5)² is a horizontal shift of the parent function f(x) = x² to the left by 5 units.

Front

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

Back

The negative sign reflects the graph of the absolute value function over the x-axis.