Absolute Value Functions Flashcard

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that contains an absolute value expression, typically in the form y = |x - a| + b, where (a, b) is the vertex of the graph.

Front

What is the vertex of the absolute value function y = |x - 3| + 2?

Back

(3, 2)

Front

Identify the axis of symmetry for the absolute value function y = |x + 1| - 4.

Back

x = -1

Front

What does the vertex represent in an absolute value function?

Back

The vertex represents the highest or lowest point of the graph, depending on whether the graph opens upwards or downwards.

Front

How does the coefficient in front of the absolute value affect the graph?

Back

If the coefficient is positive, the graph opens upwards; if negative, it opens downwards.

Front

What is the axis of symmetry for the function y = -3|x - 2| + 1?

Back

x = 2

Front

Describe the transformation of the graph y = |x| when it is changed to y = |x - 4| + 1.

Back

The graph is shifted 4 units to the right and 1 unit up.

Front

What is the vertex of the function y = -|x + 2| + 5?

Back

(-2, 5)

Front

How do you find the vertex of the absolute value function y = |x - a| + b?

Back

The vertex is located at the point (a, b).

Front

What does it mean if the graph of an absolute value function opens downwards?

Back

It means the vertex is a maximum point.