Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|bx + c| + d, where a, b, c, and d are constants.

Front

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

Back

The value of 'a' affects the vertical stretch or compression and the direction of the graph. If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of an absolute value function?

Back

The vertex of an absolute value function in the form f(x) = a|bx + c| + d is the point (-c/b, d).

Front

How do you find the vertex of the function y = -4|x + 2| + 5?

Back

To find the vertex, identify the values of c and d. Here, c = 2 and d = 5, so the vertex is (-2, 5).

Front

What does the expression |x + 2| represent on a graph?

Back

The expression |x + 2| represents a V-shaped graph that opens upwards, with the vertex at the point (-2, 0).

Front

What is the effect of adding a constant outside the absolute value function?

Back

Adding a constant outside the absolute value function shifts the graph vertically. For example, f(x) = |x| + d shifts the graph up by d units if d is positive and down if d is negative.

Front

What is the equation of the graph represented by f(x) = |x - 2|?

Back

The equation f(x) = |x - 2| represents a V-shaped graph with the vertex at (2, 0) that opens upwards.

Front

How do you determine if an absolute value function is increasing or decreasing?

Back

An absolute value function is decreasing to the left of the vertex and increasing to the right of the vertex.

Front

What is the vertex of the function y = 4|x| + 1?

Back

The vertex of the function y = 4|x| + 1 is (0, 1).

Front

What does the negative sign in front of the absolute value function indicate?

Back

The negative sign indicates that the graph opens downwards, creating a 'V' shape that points down.