1.1 Functions: Characteristics and Properties

Question 1

topic overview

Answer 1

• square of sum for a a number with a variable squared and a number
• square of sum for a number with a variable cubed and a number cubed
• finding domain and range from an equation
• finding domain and range from a graph
• stating whether a set of coorindates is function
• stating whether an equation is a function

Question 2

how to solve using the square of sum for a number with a variable squared and a number

Answer 2

requirements
-both the terms must be a number that can be squared to a real number

-there must be a minus sign between the two terms

steps

1. square root both the numbers and put in a bracket with a 2 outside, keep the minus sign
2. expand the above by putting the numbers with an addition sign in a bracket and a subtraction sign in a bracket

Question 3

how to solve using the square of sum for a number with a variable cubed and a number cubed

Answer 3

1. cubed root variable a
2. square root that answer
3. cubed root variable b
4. multiply that answer by two
5. Plug the numbers into the formula a^3+b^3= (a+b) (a^2-ab+b^2)

Question 4

algebraic model

Answer 4

a combination of variables and numbers using the operations of addition, subtraction, multiplication, and division as well as powers and roots

Question 5

dependent variable

Answer 5

a variable whose value depends on the independent

Question 6

independent variable

Answer 6

a variable that does not depend on the other

Question 7

domain

Answer 7

set of all inputs over which the function is defined

Question 8

range

Answer 8

a set of values that that function shoots out after an x value is plugged in

Question 9

function notation

Answer 9

a way to write a function that is easy to read and understand, when a function is expressed in an equation, it is written as f(x)

Question 10

graphical model

Answer 10

a function displayed on a graph

Question 11

verticle line test

Answer 11

a test that states that a graph represents a function is the line intersects the graph once and only once