McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
7. Special Functions
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Exercise 21 Page 152

Make a table of values. Then, plot and connect the obtained points.

Graph:

Domain: All real numbers.
Range: y ≥ 0

Practice makes perfect

To graph the desired function, we will make a table of values. To do so, we will assign some values to the x-variable and calculate the corresponding values for y. For simplicity, we will use even numbers so that the values of y are integers. Make sure to include positive and negative numbers, as well as zero.

x |1/2x-2| f(x)=|1/2x-2|
- 2 |1/2( - 2)-2| 3
0 |1/2( 0)-2| 2
2 |1/2( 2)-2| 1
4 |1/2( 4)-2| 0
6 |1/2( 6)-2| 1
8 |1/2( 8)-2| 2

Now, we will plot and connect the obtained points on a coordinate plane. Recall that the graph of an absolute value function has a V shape.

We see above that the x-variable can take any value. We also see that y takes values that are greater than or equal to 0. With this in mind, we can write the domain and range of the function. Domain:& all real numbers Range:& y≥ 0