Absolute Values

Domain of a Graph

Domain are the X values of the graph. Most graphs go from negative infinity to positive infinity; however, there may be a shortened domain.

In 90% of the last 30 years, the rainfall at Shell Beach has varied no more than 6.5 inches from its mean value of 24 inches. Write and solve an absolute value inequality to describe the rainfall in the other 10% of the last 30 years.

During a normal year, | X - 24 | <= 6.5 is accurate. This means that during the remaining (10%) years, | X - 24 | > 6.5

The vertex, or point, of an absolute value function can be shifted to the left.

Inside the absolute value, add a number to accomplish the left shift.

The vertex, or point, of an absolute value function can be shifted to the right.

Inside the absolute value, subtract a number to accomplish the right shift.

The vertex, or point, of an absolute value function can be shifted-up.

Outside the absolute value, add a number to accomplish the upward shift.

The vertex, or point, of an absolute value function can be shifted-down.

Outside the absolute value, subtract a number to accomplish the downward shift.

Range of a Graph

Range are the Y values of the graph. Most graphs do not go from negative infinity to positive infinity, but they may.

What are the coordinates of the highest point for the equation Y - 3 = -2 * | X - 6 |

The coordinates of the highest point are (6, 3)

What are the coordinates of the lowest point for the equation Y = | 7 - x | - 5

The coordinates of the lowest point are (7, -5)

Will this equation give you a maximum or minimum point: 4 - Y = | X + 3 |? Give the coordinates. Identify over what domain the range is increasing.

The coordinates of the maximum point are (-3, 4). The range is increasing {-infinity, -3).

Write an equation for a line passing through the coordinates (-2, 0), (-1, 1), (0, 2), and (7, 9)

The equation is Y = X + 2

Write an equation for a function passing through the points (-3, 4), (-2, 3), (0, 5), (2, 7), and (3, 8)

The equation is Y = | X + 2 | + 3

What are values?

The number, or worth, of objects.

What is the smallest value of an absolute value function?

The smallest value of an absolute value function is zero; however, a function may include an absolute value function as well as additional functions.

Find the two domains where the following statement is correct: | X + 4 | < 7

This statement means X + 4 < 7 and X + 4 > -7. For the first case to be true, X > 3. For the second case to be true, -10 < X. A joint statement be -10 < X < 3.

For what value of X do you get the smallest value of Y for the equation Y = | 3x - 9 |

What value of X gives you the smallest value of Y, and what is the value of Y, for this function: Y = | -x - 7 | + 3

A company's guidelines call for each can of soup produced not to vary from its stated volume of 14.5 fluid ounces by more than 0.07 ounces. Write and solve an absolute value inequality to describe acceptable can volumes.

| X - 14.5 | <= 0.07 This means that the amount of soup in a can can vary 14.43 < X < 14.57

Using our terms line, line segment, and vector, how can you describe a graphed absolute value function?

A graphed absolute value function consists of two vectors/rays that meet at a vertex.

What is a line?

A line is a straight object that has no end. Are there any lines in this room?

What is a line segment?

A line segment is a line that has two end points.

What is a vector?

A vector is a line that has one end point. This also can be called a Ray.

What is a vertex?

A vertex is a point where two line segments meet, or where a line changes direction. This also can be called a Point of Inflection.

What is absolute?

Absolute is a specific amount.

Graphing absolute values

Absolute value functions form a V-shape. Positive functions open-up, and negative functions open-down. The "negative" must be outside the absolute value.

What is an absolute value?

An absolute value is a specific amount/number regardless of its relative location to zero on a number line.

Increasing and Decreasing Graphs

As you move from negative infinity to positive infinity, a graph is considered "increasing" if the range goes positive, or it is "decreasing" if the range goes negative.