Absolute Value as Piecewise Functions

​2 miles

​Absolute Value

​Absolute Value

the distance from zero

​Absolute Value

the distance from zero

The absolute value of 6 is 6

​6

​Absolute Value

the distance from zero

The absolute value of 6 is 6 and is written |6|

​6

Multiple Choice

What is the absolute value of -6?

$$\left|-6\right|=?$$

• 6

• -6

• 0

​Absolute Value

the distance from zero

|-6| = 6

​6

Multiple Choice

What is the absolute value of -4?

$$\left|-4\right|=?$$

• 4

• -4

• 0

• -6

​Absolute Value

the distance from zero

|-4| = 4

​4

Math Response

Solve.

$$\left|3\right|=x$$

Type answer here

Correct Answer: 3

Deg^°

Rad

Math Response

Solve.

$$\left|-3\right|=x$$

Type answer here

Correct Answer: 3

Deg^°

Rad

Multiple Select

Solve.

$$\left|x\right|=3$$

• -3

• 3

• no solution

• 0

|x| = 3

​3

​3

​-3

​3

​|x| =

x =

Multiple Choice

Solve.

$$\left|x\right|=-2$$

• 2

• -2

• 2 and -2

• no solution

Multiple Choice

Solve.

$$\left|-13\right|=x$$

• 13

• -13

• 13 and -13

• no solution

Multiple Choice

Solve.

$$x=\left|-48\right|$$

• 48

• -48

• 48 and -48

• no solution

Multiple Choice

Solve.

$$x=\left|1.6\right|$$

• 1.6

• -1.6

• 1.6 and -1.6

• no solution

Multiple Choice

Solve.

$$5=\left|x\right|$$

• 5

• -5

• 5 and -5

• no solution

Multiple Choice

Solve.

$$-5=\left|x\right|$$

• 5

• -5

• 5 and -5

• no solution

Multiple Choice

Solve.

$$\left|x\right|=-7.5$$

• 5

• -5

• 5 and -5

• no solution

Open Ended

The function $$f\left(x\right)=\left|x\right|$$ is called the absolute value function. It is sometimes defined as giving the distance a number, x, is from zero on the number line.

In your own words, describe how you find the absolute value of a number.

Open Ended

Choose 7 integer numbers that you can see on the x-axis on the gri

Open Ended

List 7 ordered pairs using the 7 integer numbers you selected on the x-axis and write each as an ordered pair with the absolute value of x as the y value.

Example: (3,-3)

Graphing

Graph your ordered pairs.

​The graph of an absolute value function is sometimes called a Piecewise function, because the graph is in 2 linear pieces.

Multiple Choice

Give the slope (rise over ru of the red line.

• m = 1

• m = -1

• m = 0

• m = undefined

Multiple Choice

Give the y-intercept (where the graph crosses the y-axis) of the red line.

• b = 0

• b = 1

• b = -1

• there is no y-intercept

Multiple Select

Give the equation of the red line.

$$y=mx+b$$

• y = x

• y = -x

• y = 1x + 0

• x = 1

Multiple Choice

Give the equation of the blue line.

$$y=mx+b$$

• y = x

• y = -x

• y = 1x + 0

• x = 1

​for x to the left of 0 (x < 0) we would write

​for x to the right of 0 or equal to 0 (x >= 0) we would write

​So we could write f(x) = |x| as

​At Camp Joshua, a 24-mile desert hike has been planned. The hiking group plans to move at 3 miles per hour and has arranged a First Aid Station at the midpoint of the hike.