Absolute Value Functions Flashcard

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, regardless of direction. It is defined as y = |x|.

Front

What is the general form of an absolute value function?

Back

The general form is y = a|x - h| + k, where (h, k) is the vertex, 'a' determines the direction and width of the graph.

Front

What does the vertex of an absolute value function represent?

Back

The vertex is the highest or lowest point of the graph, depending on the value of 'a'. It is the point where the graph changes direction.

Front

How do you find the axis of symmetry for an absolute value function?

Back

The axis of symmetry is the vertical line that passes through the vertex, given by the equation x = h.

Front

What is the axis of symmetry for the function y = |x - 4| + 1?

Back

x = 4.

Front

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

Back

(-3, -2).

Front

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

Back

y > 2.

Front

What does the 'a' value in the absolute value function affect?

Back

The 'a' value affects the direction (upward or downward) and the steepness of the graph.

Front

If 'a' is positive in the function y = a|x - h| + k, what direction does the graph open?

Back

The graph opens upwards.

Front

If 'a' is negative in the function y = a|x - h| + k, what direction does the graph open?

Back

The graph opens downwards.