Exercise 28 Page 160

Create two tables of values and plot the graphs on the same coordinate plane.

Graph:

Comparison: See solution.

Practice makes perfect

To graph the functions without going through the entire process of transforming the parent function, we can make two tables of values. Then, we only need to plot and connect the obtained points and compare the graphs.

Graph

Let's begin with creating a table of values of function h(x).

x	\|x+5\|	Simplify	h(x)
-5	\| -5+5\|	\|0\|	0
-3	\| -3+5\|	\|2\|	2
-1	\| -1+5\|	\|4\|	4
1	\| 1+5\|	\|6\|	6

Now let's do the same with function t(x).

x	\|2x+5\|	Simplify	t(x)
-5	\|2( -5)+5\|	\|-5\|	5
-3	\|2( -3)+5\|	\|-1\|	1
-1	\|2( -1)+5\|	\|3\|	3
1	\|2( 1)+5\|	\|7\|	7

Finally, we can plot these ordered pairs on one coordinate plane.

Comparison

We can rewrite t(x) as h(2x), which is a horizontal shrink of h(x) by a factor of 12. It is being shrunk closer the y-axis. Note that when the x-values of f are two times the x-values of g, the y-values stay the same.

Subchapter links

Communicate Your Answer p.155

Monitoring Progress p.156-159

Exercises p.160-162

x	\|x+5\|	Simplify	h(x)
-5	\| -5+5\|	\|0\|	0
-3	\| -3+5\|	\|2\|	2
-1	\| -1+5\|	\|4\|	4
1	\| 1+5\|	\|6\|	6

x	\|2x+5\|	Simplify	t(x)
-5	\|2( -5)+5\|	\|-5\|	5
-3	\|2( -3)+5\|	\|-1\|	1
-1	\|2( -1)+5\|	\|3\|	3
1	\|2( 1)+5\|	\|7\|	7

Exercise 28 Page 160

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Comparison