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 axis of symmetry in an absolute value function?

Back

The axis of symmetry is a vertical line that divides the graph into two mirror-image halves. For the function y = |x - a| + b, the axis of symmetry is x = a.

Front

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

Back

The vertex of the function y = |x - a| + b is the point (a, b).

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 it opens upwards or downwards.

Front

Is the vertex of the function y = |x - 2| + 5 a maximum or minimum?

Back

The vertex (2, 5) is a minimum because the graph opens upwards.

Front

What is the effect of changing the value of 'a' in the function y = |x - a| + b?

Back

Changing 'a' shifts the graph horizontally. If 'a' increases, the graph shifts to the right; if 'a' decreases, it shifts to the left.

Front

What is the effect of changing the value of 'b' in the function y = |x - a| + b?

Back

Changing 'b' shifts the graph vertically. If 'b' increases, the graph shifts up; if 'b' decreases, it shifts down.

Front

How do you determine if the vertex is a maximum or minimum?

Back

If the absolute value function opens upwards, the vertex is a minimum. If it opens downwards, the vertex is a maximum.

Front

What is the general shape of the graph of an absolute value function?

Back

The graph of an absolute value function has a 'V' shape, with the vertex at the point where the two lines meet.

Front

For the function y = |x - 4| + 1, what is the axis of symmetry?

Back

The axis of symmetry is x = 4.