Graphing Absolute Value Functions

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|x - h| + k, where (h, k) is the vertex of the graph, 'a' determines the direction and steepness of the graph.

Front

How does the value of 'a' affect the graph of an absolute value function?

Back

The value of 'a' affects the direction and steepness of the graph. If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards. The larger the absolute value of 'a', the steeper the graph.

Front

What does the vertex of an absolute value function represent?

Back

The vertex of an absolute value function represents the minimum or maximum point of the graph, depending on the value of 'a'.

Front

How do you find the vertex of the function f(x) = -2|x + 3| + 5?

Back

To find the vertex, rewrite the function in vertex form: f(x) = -2|x - (-3)| + 5. The vertex is at (-3, 5).

Front

What is the effect of the transformation 'x + 3' in the function f(x) = -2|x + 3| + 5?

Back

The transformation 'x + 3' shifts the graph 3 units to the left.

Front

What does the transformation '+ 5' do to the graph of an absolute value function?

Back

The transformation '+ 5' shifts the graph 5 units upward.

Front

How do you graph the function y = |x - 2|?

Back

To graph y = |x - 2|, plot the vertex at (2, 0) and create a V-shape opening upwards, with points on either side of the vertex.

Front

What is the equation of the graph that opens downwards and has a vertex at (0, 0)?

Back

The equation is y = -|x|.

Front

How do you determine the x-intercepts of the function y = |x + 2|?

Back

To find the x-intercepts, set y = 0: 0 = |x + 2|. This gives x + 2 = 0, so x = -2.

Front

What is the significance of the absolute value in the function y = |x|?

Back

The absolute value ensures that the output is always non-negative, creating a V-shape graph that reflects points across the x-axis.