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Big Ideas Math Algebra 1, 2015

BI

Big Ideas Math Algebra 1, 2015 View details

7. Graphing Absolute Value Functions

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Exercise 32 Page 160

Create two tables of values and then 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 the ordered pairs that we find.

Graph

Let's begin with creating a table of values of function $u .$

$x$	$∣ x - 1 ∣ + 2$	Simplify	$u (x)$
$- 3$	$∣ - 3 - 1 ∣ + 2$	$∣ - 4 ∣ + 2$	$6$
$- 1$	$∣ - 1 - 1 ∣ + 2$	$∣ - 2 ∣ + 2$	$4$
$1$	$∣ 1 - 1 ∣ + 2$	$∣ 0 ∣ + 2$	$2$
$3$	$∣ 3 - 1 ∣ + 2$	$∣ 2 ∣ + 2$	$4$

Now let's do the same with function $v .$

$x$	$∣ ∣ ∣ ∣ ∣ - \frac{1}{2} x - 1 ∣ ∣ ∣ ∣ ∣ + 2$	Simplify	$v (x)$
$- 4$	$∣ ∣ ∣ ∣ ∣ - \frac{1}{2} (- 4) - 1 ∣ ∣ ∣ ∣ ∣ + 2$	$∣ 1 ∣ + 2$	$3$
$- 2$	$∣ ∣ ∣ ∣ ∣ - \frac{1}{2} (- 2) - 1 ∣ ∣ ∣ ∣ ∣ + 2$	$∣ 0 ∣ + 2$	$2$
$2$	$∣ ∣ ∣ ∣ ∣ - \frac{1}{2} (2) - 1 ∣ ∣ ∣ ∣ ∣ + 2$	$∣ - 2 ∣ + 2$	$4$
$4$	$∣ ∣ ∣ ∣ ∣ - \frac{1}{2} (4) - 1 ∣ ∣ ∣ ∣ ∣ + 2$	$∣ - 3 ∣ + 2$	$5$

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

Comparison

We can rewrite $v (x)$ as $u (- \frac{1}{2} x),$ which is a horizontal stretch by a factor of $2$ followed by a reflection in the $y -$ axis. Note that the $y -$ intercept is the same for both graphs.

Subchapter links

Communicate Your Answer p.155

Monitoring Progress p.156-159

Exercises p.160-162