explain me functions chapter
Answers
Answer:
Summary: Characteristics of Functions and Their Graphs
Key Equations
Constant function
f
(
x
)
=
c
, where
c
is a constant
Identity function
f
(
x
)
=
x
Absolute value function
f
(
x
)
=
|
x
|
Quadratic function
f
(
x
)
=
x
2
Cubic function
f
(
x
)
=
x
3
Reciprocal function
f
(
x
)
=
1
x
Reciprocal squared function
f
(
x
)
=
1
x
2
Square root function
f
(
x
)
=
√
x
Cube root function
f
(
x
)
=
3
√
x
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.
Function notation is a shorthand method for relating the input to the output in the form
y
=
f
(
x
)
.
In table form, a function can be represented by rows or columns that relate to input and output values.
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.
To solve for a specific function value, we determine the input values that yield the specific output value.
An algebraic form of a function can be written from an equation.
Input and output values of a function can be identified from a table.
Relating input values to output values on a graph is another way to evaluate a function.
A function is one-to-one if each output value corresponds to only one input value.
A graph represents a function if any vertical line drawn on the graph intersects the graph at no more than one point.
A graph represents a one-to-one function if any horizontal line drawn on the graph intersects the graph at no more than one point.
Glossary
dependent variable
an output variable
domain
the set of all possible input values for a relation
function
a relation in which each input value yields a unique output value