parent functions and transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, representing the basic shape of the graph.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is y = x².

Front

How does the graph of y = -x² differ from y = x²?

Back

The graph of y = -x² is a reflection of y = x² over the x-axis.

Front

What transformation is represented by y = (x - 3)²?

Back

The graph is translated right 3 units.

Front

What is the parent function of an absolute value function?

Back

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

Front

How does the graph of y = |x| change when it is shifted up 2 units?

Back

The new function is y = |x| + 2, which moves the entire graph up.

Front

What type of function is represented by the equation y = 2^x?

Back

This is an exponential function.

Front

What is the effect of a negative sign in front of a function, such as y = -|x|?

Back

It reflects the graph over the x-axis.

Front

What transformation occurs in the function y = x² - 2?

Back

The graph is translated down 2 units.

Front

Identify the type of function: y = 3x + 1.

Back

This is a linear function.