Absolute Value

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is y = |x|.

Front

How does the graph of y = |x| look?

Back

The graph of y = |x| is a V-shaped graph that opens upwards.

Front

What effect does a negative sign in front of the absolute value function have on the graph?

Back

A negative sign reflects the graph over the x-axis.

Front

What does the equation y = |x - 7| - 2 represent in terms of transformations?

Back

This equation represents a horizontal shift to the right by 7 units and a vertical shift down by 2 units.

Front

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

Back

The vertex is located at the point (h, k).

Front

What does the 'a' value in the equation y = a|x - h| + k indicate?

Back

The 'a' value indicates the vertical stretch or compression and the direction of the graph (upward if a > 0, downward if a < 0).

Front

What is the transformation of the function y = -2|x - 3| + 1 from the parent function?

Back

The function is reflected over the x-axis, stretched vertically by a factor of 2, shifted right by 3 units, and shifted up by 1 unit.

Front

What is the significance of the vertex in an absolute value graph?

Back

The vertex represents the minimum or maximum point of the graph, depending on the direction it opens.

Front

How do you determine the x-intercepts of the absolute value function y = |x - h| + k?

Back

Set y = 0 and solve for x: |x - h| + k = 0.