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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.
Got questions? Get instant answers now!
Questions & Answers
If c is the cost function for a particular product, find the marginal cost functions and their
values at x=10 a. c(x) = 800+ 0.04x + 0.0002x² b. c(x) = 250 + 100x + 0.001x²
how can I find set theory
how can I find set theory
Jarvis
is there an error on the one about the dime's thickness? says 2.2x10⁶=0.00135 m
hi, interested in algebra
how to reduce an equation?
Makan
by manipulation of both side
Al
9(y+8)-27 is 9y+45.
Why can't you reduce that to y+5? I know that's wrong but can't explain why
when you reduce an equation to its simplest terms, you can't change the value of the equation. reducing it to y + 5 is equivalent to dividing it by 9 which changes the value. you can multiply it by 1 or 9/9 which would give 9(y + 5). multiplying it by one does not change the value.
Philip
Given a polynomial expression, factor out the greatest common factor.
WHAT IS QUADRATIC EQUATION?
WHAT IS SYSTEM OF LINEAR INEWUALITIES?
Charles
WHAT IS SYSTEM OF LINEAR INEWUALITIES?
Charles
what are equations?
Charles
Definition of economics according to
karl Marx
Thomas malthus
Jeremy bentham
David Ricardo
J.K
Rakiya
Please help me is assignment
Rakiya
The 47th problem of Euclid
Kenneth
show that the set of all natural number form semi group under the composition of addition
what is the meaning
Dominic
explain and give four Example hyperbolic function
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the
fraction, the value of the fraction becomes 2/3. Find the original fraction.
2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2
-------------- = _
x + 9 + 6 3
x + 6 3
----------- x -- (cross multiply)
x + 15 2
3(x + 6) = 2(x + 15)
3x + 18 = 2x + 30 (-2x from both)
x + 18 = 30 (-18 from both)
x = 12
Test:
12 + 6 18 2
-------------- = --- = ---
12 + 9 + 6 27 3
Pawel
2.
(x) + (x + 2) = 60
2x + 2 = 60
2x = 58
x = 29
29, 30, & 31
Pawel
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Q2
x+(x+2)+(x+4)=60
3x+6=60
3x+6-6=60-6
3x=54
3x/3=54/3
x=18
:. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1
x + 3x + 1 = 113
4x = 112, x = 28
Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
please can go further on polynomials quadratic
Abdullahi
I need quadratic equation link to Alpa Beta
Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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