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We will see these toolkit functions, combinations of toolkit functions, their graphs, and their transformations frequently throughout this book. It will be very helpful if we can recognize these toolkit functions and their features quickly by name, formula, graph, and basic table properties. The graphs and sample table values are included with each function shown in
[link] .
Toolkit Functions |
Name |
Function |
Graph |
Constant |
where
is a constant |
|
Identity |
|
|
Absolute value |
|
|
Quadratic |
|
|
Cubic |
|
|
Reciprocal |
|
|
Reciprocal squared |
|
|
Square root |
|
|
Cube root |
|
|
Key equations
Constant function |
where
is a constant |
Identity function |
|
Absolute value function |
|
Quadratic function |
|
Cubic function |
|
Reciprocal function |
|
Reciprocal squared function |
|
Square root function |
|
Cube root function |
|
Key concepts
- A relation is a set of ordered pairs. A function is a specific type of relation in which each domain value, or input, leads to exactly one range value, or output. See
[link] and
[link] .
- Function notation is a shorthand method for relating the input to the output in the form
See
[link] and
[link] .
- In tabular form, a function can be represented by rows or columns that relate to input and output values. See
[link] .
- To evaluate a function, we determine an output value for a corresponding input value. Algebraic forms of a function can be evaluated by replacing the input variable with a given value. See
[link] and
[link] .
- To solve for a specific function value, we determine the input values that yield the specific output value. See
[link] .
- An algebraic form of a function can be written from an equation. See
[link] and
[link] .
- Input and output values of a function can be identified from a table. See
[link] .
- Relating input values to output values on a graph is another way to evaluate a function. See
[link] .
- A function is one-to-one if each output value corresponds to only one input value. See
[link] .
- A graph represents a function if any vertical line drawn on the graph intersects the graph at no more than one point. See
[link] .
- The graph of a one-to-one function passes the horizontal line test. See
[link] .
Section exercises
Verbal
What is the difference between a relation and a function?
A relation is a set of ordered pairs. A function is a special kind of relation in which no two ordered pairs have the same first coordinate.
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Why does the vertical line test tell us whether the graph of a relation represents a function?
When a vertical line intersects the graph of a relation more than once, that indicates that for that input there is more than one output. At any particular input value, there can be only one output if the relation is to be a function.
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Questions & Answers
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Omeprazole
Cimetidine / Tagament
For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
how does the stomach protect itself from the damaging effects of HCl
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
function of digestive
Ali
what is the normal body temperature
please why 37 degree selcius normal temperature
Mark
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
how does Lysin attack pathogens
Diya
I information on anatomy position and digestive system and there enzyme
anatomy of the female external genitalia
Organ Systems Of The Human Body (Continued)
Organ Systems Of The Human Body (Continued)
what's lochia albra
Kizito
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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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