1.6 Absolute value functions  (Page 5/7)

How do you solve an absolute value equation?

How can you tell whether an absolute value function has two x -intercepts without graphing the function?

When solving an absolute value function, the isolated absolute value term is equal to a negative number. What does that tell you about the graph of the absolute value function?

How can you use the graph of an absolute value function to determine the x -values for which the function values are negative?

How do you solve an absolute value inequality algebraically?

Describe all numbers $x$ that are at a distance of 4 from the number 8. Express this using absolute value notation.

Describe all numbers $x$ that are at a distance of $\frac{1}{2}$ from the number −4. Express this using absolute value notation.

Describe the situation in which the distance that point $x$ is from 10 is at least 15 units. Express this using absolute value notation.

Find all function values $f(x)$ such that the distance from $f(x)$ to the value 8 is less than 0.03 units. Express this using absolute value notation.

$|x+3|=9$

$|6-x|=5$

$|5x-2|=11$

$|4x-2|=11$

$2|4-x|=7$

$3|5-x|=5$

$3|x+1|-4=5$

$5\left|x-4\right|-7=2$

$0=-\left|x-3\right|+2$

$2\left|x-3\right|+1=2$

$\left|3x-2\right|=7$

$\left|3x-2\right|=-7$

$\left|\frac{1}{2}x-5\right|=11$

$\left|\frac{1}{3}x+5\right|=14$

$-\left|\frac{1}{3}x+5\right|+14=0$

$f(x)=2\left|x+1\right|-10$

$f(x)=4\left|x-3\right|+4$

$f(x)=-3\left|x-2\right|-1$

$f(x)=-2\left|x+1\right|+6$

$\left|x-2\right|>10$

$2\left|v-7\right|-4\ge 42$

$\left|3x-4\right|\le 8$

$\left|x-4\right|\ge 8$

$\left|3x-5\right|\ge 13$

$\left|3x-5\right|\ge -13$

$\left|\frac{3}{4}x-5\right|\ge 7$

$\left|\frac{3}{4}x-5\right|+1\le 16$

$y=|x-1|$

$y=|x+1|$

$y=\left|x\right|+1$

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

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

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

$y=-\left|x-3\right|-2$

$f(x)=-|x-1|-2$

$f(x)=-|x+3|+4$

$f(x)=2|x+3|+1$

$f(x)=3\left|x-2\right|+3$

$f(x)=\left|2x-4\right|-3$

$f\left(x\right)=\left|3x+9\right|+2$

$f(x)=-\left|x-1\right|-3$

$f(x)=-\left|x+4\right|-3$

$f(x)=\frac{1}{2}\left|x+4\right|-3$

Use a graphing utility to graph $f(x)=10|x-2|$ on the viewing window $\left[0,4\right].$ Identify the corresponding range. Show the graph.

Use a graphing utility to graph $f(x)=-100\left|x\right|+100$ on the viewing window $\left[-5,5\right].$ Identify the corresponding range. Show the graph.

$f(x)=-0.1\left|0.1(0.2-x)\right|+0.3$

$f(x)=4\times {10}^9\left|x-(5\times {10}^9)\right|+2\times {10}^9$

$|-2x-\frac{2}{3}(x+1)|+3>\mathrm{-1}$

If possible, find all values of $a$ such that there are no $x\text{-}$ intercepts for $f(x)=2\left|x+1\right|+a.$

If possible, find all values of $a$ such that there are no $y$ -intercepts for $f(x)=2\left|x+1\right|+a.$

Cities A and B are on the same east-west line. Assume that city A is located at the origin. If the distance from city A to city B is at least 100 miles and $x$ represents the distance from city B to city A, express this using absolute value notation.

The true proportion $p$ of people who give a favorable rating to Congress is 8% with a margin of error of 1.5%. Describe this statement using an absolute value equation.

Students who score within 18 points of the number 82 will pass a particular test. Write this statement using absolute value notation and use the variable $x$ for the score.

A machinist must produce a bearing that is within 0.01 inches of the correct diameter of 5.0 inches. Using $x$ as the diameter of the bearing, write this statement using absolute value notation.

The tolerance for a ball bearing is 0.01. If the true diameter of the bearing is to be 2.0 inches and the measured value of the diameter is $x$ inches, express the tolerance using absolute value notation.