Ch4 Chapter Review

Question 1

There are 3 ways to represent a linear equation. They are ?

Answer 1

1. Tables can be used to represent it
2. Graph can be used to represent it
3. Equations can be used to represent it

And we can transform from one form to another!

Question 2

From Table to Equation:

How write a linear equation from a table of data pairs?

Question 3

From Graph to Equation

How to write an equation from a graph line?

Question 4

From Equation to Table

How to make a table from an equation?

Question 5

From Equation to Graph

How to draw a line using equation?

Question 6

From Table to Graph

How to draw a line using table?

Question 7

Review: how to draw Slope-Intercept form:y=mx +b

like: y = 2x+1

Question 8

Review: how to draw Point-Slope form:y-y1 = m(x-x1)

like: y-2 = 2(x-1)

Question 9

Review: how to calculate slope using a table?

Question 10

Concept: what does a relation mean?

Answer 10

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.

Question 11

Concept: What does the Domain mean?

Answer 11

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.

Question 12

Concept: What does the Range mean?

Answer 12

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,

Question 13

What is a function?

How to represent a function?

Answer 13

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.

Question 14

What is a function?

How to represent a function?

Answer 14

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.

Question 16

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?

Answer 16

independent variable: n

dependent variable:m

equation m= 20n represents “the total money m you can earn for mowing n pieces of lawns”.

Question 17

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?

Answer 17

independent variable: h

dependent variable:d

equation d=4.5h represents “the total distance d Ray can walk in h hours”.

Question 18

What is the Function Table?

Answer 18

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).

Question 19

Make function table for f(x)=x+5.

Then state the domain and the range for this function

Answer 19

the domain is the set of the input value, stated as:

____________________________________

the range is the set of output values, stated as:

_____________________________________

Question 20

Make function table for f(x)=x+5.

Then state the domain and the range for this function

Answer 20

the domain is the set of the input value, stated as:

____________________________________

the range is the set of output values, stated as:

_____________________________________

Question 21

What is the Function Table?

Answer 21

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).

Question 22

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”

Answer 22

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

Question 23

Find each function value:

1. f(2) if f(x) =x-4
2. f(12) if . f(x)=1/2x+5

Question 24

Find each function value:

1. f(2) if f(x) =x-4
2. f(12) if . f(x)=1/2x+5

Question 25

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”

Answer 25

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

Question 26

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?

Answer 26

independent variable: h dependent variable:d equation d=4.5h represents "**the total distance d Ray can walk in h hours**".

Question 27

**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?

Answer 27

independent variable: n dependent variable:m equation m= 20n represents "**the total money m you can earn for mowing n pieces of lawns**".

Question 28

How to graph a Function?

Answer 28

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.

Question 29

What is a linear function?

Answer 29

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**.