Week 3: Absolute Values – Day 5

Maxima and Minima

For each of these absolute value functions: is there an absolute maximum, minimum, or neither? If there is a minimum or maximum, specify the x value where it is located.

1. f(x) = |x| + 1

2. f(x) = |x – 1|

3. f(x) = 1 – |x|

4. f(x) = 1 – |2x|

5. f(x) = |x| + |x – 1|

Bonus question: graph the function in #5.

Week 3: Absolute Values – Day 4

Intersections of Absolute Value Functions

Two absolute value functions are given. Find their intersection points. In every case, it helps to quickly sketch the graph to know what to expect.

1. f(x) = |x| and g(x) = 1 – |x|

2. f(x) = |x| and g(x) = |x – 3|

3. f(x) = |x|  and g(x) = |2x| – 4

4. f(x) = |x| and g(x) = |x – 3|/2

5. f(x) = |x + 1| and g(x) = |x – 1|

|/4

5.

Week 3: Absolute Values – Day 3

The Absolute Value Function

Sketch the graphs of the following absolute value functions.

1. y = f(x) = |x| + 1

2. y = g(x) = |x + 1|

3. y = h(x) = 1 – |x|

4. y = p(x) =  – |x – 2|

5. y = q(x) = 3|x|

Week 3: Absolute Values – Day 2

Solving Inequalities

Solve and graph each inequality on the number line.

1.  |x – 2| < 1.

2. |x + 3| > 6

3. |2x| =< 8    (“=<” means “less than or equal to”)

4. 5 – |x – 2| >= 1    (“>=” means “greater than or equal to”)

5. 3|2x + 1| < 9

Week 3: Absolute Values – Day 1

As Distances

The absolute value of x can be interpreted as its distance from zero. Similarly, |x – 5| is the distance of the number x from 5. Interpret the following absolute value expressions as distances.

1. |x – 10|

2. |x + 4|

3. |6x|

4. |2 – x|

5. |2 + x|