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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
how does Neisseria cause meningitis
is the branch of biology that deals with the study of microorganisms.
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
How bacteria create energy to survive?
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
which site have a normal flora
Many sites of the body have it
Skin
Nasal cavity
Oral cavity
Gastro intestinal tract
Safaa
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
part of a tissue or an organ being wounded or bruised.
Wilfred
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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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