Graphing Absolute Value Functions

Front

What is the domain of the graph of an absolute value function?

Back

The domain of the graph of an absolute value function is (-∞, ∞).

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is y = |x - h| + k, where (h, k) is the vertex of the graph.

Front

What does the vertex of an absolute value function represent?

Back

The vertex represents the minimum or maximum point of the graph, depending on the orientation.

Front

How does the graph of y = |x| differ from y = |x + 2|?

Back

The graph of y = |x + 2| is shifted 2 units to the left compared to y = |x|.

Front

What is the effect of the '+ k' in the equation y = |x| + k?

Back

The '+ k' shifts the graph vertically by k units. If k is positive, the graph shifts up; if negative, it shifts down.

Front

What is the effect of the '- k' in the equation y = |x| - k?

Back

The '- k' shifts the graph vertically down by k units.

Front

What is the range of the graph of an absolute value function?

Back

The range of the graph of an absolute value function is [k, ∞) if the vertex is at (h, k).

Front

How do you determine the range of a graph?

Back

The range is determined by reading the ends of the graph from bottom to top.

Front

What does the graph of y = |x - 2| look like?

Back

The graph is a V-shape with the vertex at (2, 0) and opens upwards.

Front

What is the effect of the coefficient in front of the absolute value function, such as in y = a|x|?

Back

The coefficient 'a' affects the vertical stretch or compression of the graph. If a > 1, the graph stretches; if 0 < a < 1, it compresses.