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- Algebra and trigonometry
- Functions
- Absolute value functions
Key concepts
- Applied problems, such as ranges of possible values, can also be solved using the absolute value function. See
[link] .
- The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction. See
[link] .
- In an absolute value equation, an unknown variable is the input of an absolute value function.
- If the absolute value of an expression is set equal to a positive number, expect two solutions for the unknown variable. See
[link] .
Section exercises
Verbal
How do you solve an absolute value equation?
Isolate the absolute value term so that the equation is of the form
Form one equation by setting the expression inside the absolute value symbol,
equal to the expression on the other side of the equation,
Form a second equation by setting
equal to the opposite of the expression on the other side of the equation,
Solve each equation for the variable.
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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?
The graph of the absolute value function does not cross the
-axis, so the graph is either completely above or completely below the
-axis.
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Algebraic
Find all function values
such that the distance from
to the value 8 is less than 0.03 units. Express this set of numbers using absolute value notation.
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For the following exercises, find the
x - and
y -intercepts of the graphs of each function.
Graphical
For the following exercises, graph the absolute value function. Plot at least five points by hand for each graph.
For the following exercises, graph the given functions by hand.
Technology
Use a graphing utility to graph
on the viewing window
Identify the corresponding range. Show the graph.
range:
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For the following exercises, graph each function using a graphing utility. Specify the viewing window.
Extensions
For the following exercises, solve the inequality.
If possible, find all values of
such that there are no
-intercepts for
There is no solution for
that will keep the function from having a
-intercept. The absolute value function always crosses the
-intercept when
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Real-world applications
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
represents the distance from city B to city A, express this using absolute value notation.
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The true proportion
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.
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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
for the score.
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A machinist must produce a bearing that is within 0.01 inches of the correct diameter of 5.0 inches. Using
as the diameter of the bearing, write this statement using absolute value notation.
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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
inches, express the tolerance using absolute value notation.
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Questions & Answers
what does preconceived mean
How can I develope my cognitive domain
why is communication effective
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
compare and contrast skinner's perspective on personality development on freud
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
interpersonal relationships
What would be the best educational aid(s) for gifted kids/savants?
treat them normal, if they want help then give them.
that will make everyone happy
Saurabh
What are the treatment for autism?
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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