Algebra 2: Parent Functions and Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear, quadratic, cubic, absolute value, and square root functions.

Front

What is the equation of the absolute value parent function?

Back

The equation of the absolute value parent function is y = |x|.

Front

How does shifting a graph to the right affect its equation?

Back

Shifting a graph to the right by 'h' units involves replacing 'x' with 'x - h' in the function's equation.

Front

What is the equation of the square root parent function?

Back

The equation of the square root parent function is y = √x.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants.

Front

How do you translate a quadratic function left by 'h' units?

Back

To translate a quadratic function left by 'h' units, replace 'x' with 'x + h' in the function's equation.

Front

What is the equation of the cubic parent function?

Back

The equation of the cubic parent function is y = x³.

Front

What is the effect of a vertical stretch on a parent function?

Back

A vertical stretch multiplies the output of the function by a factor greater than 1, making the graph steeper.

Front

What is the equation of a transformed quadratic function that opens upwards?

Back

The equation of a transformed quadratic function that opens upwards is y = a(x - h)² + k, where 'a' > 0, (h, k) is the vertex.

Front

What is the difference between even and odd functions?

Back

Even functions are symmetric about the y-axis (f(x) = f(-x)), while odd functions are symmetric about the origin (f(-x) = -f(x)).