Ch4 Chapter Review Flashcards
There are 3 ways to represent a linear equation. They are ?
- Tables can be used to represent it
- Graph can be used to represent it
- Equations can be used to represent it
And we can transform from one form to another!
From Table to Equation:
How write a linear equation from a table of data pairs?
From Graph to Equation
How to write an equation from a graph line?
From Equation to Table
How to make a table from an equation?
From Equation to Graph
How to draw a line using equation?
From Table to Graph
How to draw a line using table?
Review: how to draw Slope-Intercept form:y=mx +b
like: y = 2x+1
Review: how to draw Point-Slope form:y-y1 = m(x-x1)
like: y-2 = 2(x-1)
Review: how to calculate slope using a table?
Concept: what does a relation mean?
A relation is a mathematical process or rules that maps elements from one set, called the domain, to another set (which could be the same set) called the range. When a relation is drawn as a graph, the domain is always on the x-axis and the range is always on the y-axis.
A function is a special type of relation, where every element of the domain maps to exactly one element of the range.
Concept: What does the Domain mean?
In algebra, Domain is simply the set of elements (which could be numbers or other values) which are used as input for a relation.
We also say that the domain is the independent variable.
Concept: What does the Range mean?
In algebra, Range is the set of elements (which could be numbers or other values) which are used as output for a relation.
We also say that the range is the dependent variable,
What is a function?
How to represent a function?
A function is a relation in which every member of the domain(input value) is paired with exactly one member of the range( output value).
You can think of Function just like a calculator, you type in a number as input, then calculator calculates and give another number as output.
A function, as a kind of relation, can be represented as equation, function table,graph, and word statement.
What is a function?
How to represent a function?
A function is a relation in which every member of the domain(input value) is paired with exactly one member of the range( output value).
You can think of Function just like a calculator, you type in a number as input, then calculator calculates and give another number as output.
A function, as a kind of relation, can be represented as equation, function table,graph, and word statement.
Independent Variables can change by itself.
Dependent Variable change because of other variables.
In the function of m =20n, here m represent the amount of money earned and n represents the number of lawns mowed. so in this example
which is the dependent variable?
which is the independent variable?
what does m=20n mean?
independent variable: n
dependent variable:m
equation m= 20n represents “the total money m you can earn for mowing n pieces of lawns”.
In the function of d =4.5h, here d represents the distance Ray can walk, 4.5 represent Ray’s speed. h represent how many hours Ray walks.
which is the dependent variable?
which is the independent variable?
what does d=4.5h mean?
independent variable: h
dependent variable:d
equation d=4.5h represents “the total distance d Ray can walk in h hours”.
What is the Function Table?
Function Table is one way of representing a function. We organize thing below as a table:
value of input(the domain, or independent variable), calculating expression(how to calculate output value),
and value of output(range, or dependent variable).
Make function table for f(x)=x+5.
Then state the domain and the range for this function
the domain is the set of the input value, stated as:
____________________________________
the range is the set of output values, stated as:
_____________________________________
Make function table for f(x)=x+5.
Then state the domain and the range for this function
the domain is the set of the input value, stated as:
____________________________________
the range is the set of output values, stated as:
_____________________________________
What is the Function Table?
Function Table is one way of representing a function. We organize thing below as a table:
value of input(the domain, or independent variable), calculating expression(how to calculate output value),
and value of output(range, or dependent variable).
How to find the value of a function for a certain number?
example here: f(x) = 15x, how to find f(2)?
note: f(x) should be read as “the function of x”
just replace variable x by the given number in the equation, then you can find the f(x).
example: to find f(2), you replace x by 2,so
f(2) = 15x2
=30
Find each function value:
- f(2) if f(x) =x-4
- f(12) if . f(x)=1/2x+5
Find each function value:
- f(2) if f(x) =x-4
- f(12) if . f(x)=1/2x+5
How to find the value of a function for a certain number?
example here: f(x) = 15x, how to find f(2)?
note: f(x) should be read as “the function of x”
just replace variable x by the given number in the equation, then you can find the f(x).
example: to find f(2), you replace x by 2,so
f(2) = 15x2
=30
In the function of d =4.5h, here d represents the distance Ray can walk, 4.5 represent Ray’s speed. h represent how many hours Ray walks.
which is the dependent variable?
which is the independent variable?
what does d=4.5h mean?
independent variable: h
dependent variable:d
equation d=4.5h represents “the total distance d Ray can walk in h hours”.
Independent Variables can change by itself.
Dependent Variable change because of other variables.
In the function of m =20n, here m represent the amount of money earned and n represents the number of lawns mowed. so in this example
which is the dependent variable?
which is the independent variable?
what does m=20n mean?
independent variable: n
dependent variable:m
equation m= 20n represents “the total money m you can earn for mowing n pieces of lawns”.
How to graph a Function?
Like equations, functions can be represented in words,table, graph, and also as ordered pairs.
And the graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
So how to draw a function?
We just find out the ordered pairs of the function, and then use these pairs as coordinates of points and connect these points.
What is a linear function?
A linear function is a function in which the graph of the solutions forms a straight line.
If the value of the function is Continuous Data, then we graph the function using a solid line.
If the value of the function is Discrete Data, then we graph the function using Dots.
