Math 2nd Quarter
"At most how many types of cards can a man buy if he only has ₱750 in his wallet?"
It means the value should be less than or equal to the given amount. Thus, we use the symbol ≤
The expression 3x + 2 > 5y is an example of
Linear Inequality in two variables
A cheetah can cover a distance of 120 miles in 1 hour. Which of the following functions determine how many miles a cheetah can cover in x number of hours.
Multiply x (number of hours) by the rate at which the cheetah can cover distance in an hour. f(x) = 120x
Consider the statement 'If a number is an integer, then it is a rational number.' Is its converse true?
No
onsider the statement 'I am an Asian if I am a Filipino.' When this statement is rewritten in if-then form and its inverse is obtained, is the inverse true?
No
A shoe manufacturer produces shoes at a cost of ₱ 800 per shoe. Express the profit gained by selling x numbers of shoes if each shoe is sold at ₱1300.
P(x) = 500x
Determine the dependent variable in the function defined by the equation y=x+2
The value of y depends on the choice of x.
"Zen wants to eat 2 types of meal not greater than ₱150."
The value should be less than or equal to ₱150. Thus, we use the symbol ≤.
Determine the independent variable in the function defined by the equation y=x+2.
The variable x is the independent variable because its value does not depend on anything.
Write the inverse of the statement'x+5=3 when x=−2'.
Therefore, the inverse of the if-then statement is 'If x≠−2, then x+5≠3.'
Determine if the following statement is true or false:The if-then form of 'When it rains, it pours.' is 'If it rains, then it pours.'.
True
In a function, an x value must only be paired with a unique value of y. However, a distinct y value can be paired with multiple values of x.
True
The expression 5−5a≠3e is a linear inequality in two variables.
True
The inequality 10x+5y≥200 describes the situation: Pete sells guavas and atis for ₱10 and ₱5 each, respectively. If he wants to earn not less than ₱200 how many of each guavas and atis does he needs to sell?
True
The inverse of the statement 'Henry will not attend the seminar if he is busy.' is 'Henry will attend the seminar if he is not busy.'.
True
The inverse of the statement 'If I will not swim, then I will not go.' is 'If I will swim, then I will go'.
True
The inverse of the statement 'If I will sing, then it will rain'" is 'If I will not sing then, it will not rain.'.
True
system of linear inequalities in two variables is composed of two or more linear inequalities.
True
The algebraic sentence 4/3x−7≥3y is a linear inequality in two variables.
True, it uses the right symbol and has two variables both of the first degree
How can we descive the relation of one set to another?
We can describe the relation of one set to another as a diagram that illustrates which element(s) of the first set correspond(s) to which element(s) of the second set.
Determine which of the following ordered pairs is not an element of the relation defined by y=x−2
When x=0, the value of y should be −2.
Is the statement 'If it rains, then I will not leave.' in if-then form?
Yes
Equation
a rule by which a unique value of is assigned to a value of x.
Function
a set of ordered pairs wherein an x value must only be paired with a unique value of y.
An if-then statement or a conditional statement
a statement that is composed of a hypothesis and a conclusion and is denoted as where is the hypothesis, and is the conclusion. This is read as "if , then ".
independent variable
a variable (often denoted by x ) whose variation does not depend on that of another.
dependent variable
a variable (often denoted by y ) whose value depends on that of another.
Test point
any point that lies on the Cartesian plane for which we test if the inequality holds true.
It is the result of the condition.
conclusion
the points on the boundary line itself are not included in the solution set of the inequality
dashed boundary line
The boundary line can either be
dashed or solid
Rise
described as the change in (going up or down)
What do we call the set of all admissible values of x for any function f(x)?
domain of a function
Dashed boundary lines
represent the inequality that uses the relation symbols "<" and ">"
solid boundary line
represent those that use the relation symbols "≤ " and "≥ "
Identify the linear inequality for this situation: Bill has 90 feet of fencing materials. He wants to fence a rectangular plot of land.
represented by 2x+2y≤90
The shaded region
represents the solution set region on the graph
Boundary Line
separates the solution points from non-solution points.
the points on the boundary line itself are part of the solution set.
solid boundary line
dentify the relation symbol to be used in the expression: "How many candies and bubble gums can you buy if you have at least ₱20?"
symbol ≥ is used because of the phrase "at least."
Run
the change in (going left or right)
y-intercept
the corresponding value of the function f(x)when x = 0
intersection of the solution regions
the graph of the solution set of a system of linear inequalities in two variables of the two linear inequalities in the system
x-intercept
the value of x when f(x) = 0
The most common way to write a function
using the f(x) notation (read as "f of x").
How can we think of a relation as a collection of values represented as ordered pairs?
where the first element of each pair is related in some manner to the second element of the pair.
Which of the following equations define a relation wherein the value of y is obtained by taking the square of the assigned value of x.
y = x^2
Which of the following ordered pairs is not in the graph of the linear function f(x)=x/4+1?
(0, -1)
Which of the following ordered pairs is not an element of the function f(x)=x−5?
(0,5)
The population growth in a certain village is modeled by the linear function f(t)=10t+50 where t is the number of years after the village was founded. What is the population in the village after 3 years?
80
Not a symbol for inequality
=
Give a linear inequality that best describes the graph.
By using the intercepts (3,0) and (0,3) write the equation of the line then determine the relation symbol to be used.
A farmer is planning to construct a fence around his farm. The length of the farm is 2 meters longer than twice the width. Express the cost of building the fence as a function of x (in meters), if 1 meter of fence costs ₱80.
C = 480x + 320
The inverse of some if-then statement is 'Ferry cannot go to China because she does not have a passport.'. Which of the following is the original if-then statement?
If Ferry has a passport, then she can go to China.'
Choose the converse of the statement 'If I am driving alone, then I can go home anytime'.
If I can go home anytime, then I am driving alone.'
Rewrite the statement in if-then form:'I will leave early so that I won't be late.'
If I will leave early, then I will not be late
Rewrite the following statement in if-then form:A pentagon has five sides.
If a polygon is a pentagon, then it has five sides
Rewrite the following statement in if-then form:All dogs hate cats.
If an animal is a dog, then it hates cats.
merry-go-round can complete 1 revolution in 1 minute. Write a function that represents how many revolutions the merry-go-round can complete in x number of minutes.
If the merry-go-round can complete a revolution in 1 minute, then it can complete 2 revolutions in 2 minutes, 3 revolutions in 3 minutes, and so forth. Therefore, the number of revolutions it can complete in x number of minutes is given by the function f(x)=x.
Rewrite the statement:x+5=3 when x=−2.
If x=−2, then x+5=3.
What is the y - intercept of the linear function y=5x−1?
-1
In a function, it is the set of all possible values of the dependent variable.
range of a function
Which of the following equations represents a linear function?
A linear function is a function that can be written in the form y=mx+b . In this case m=1 and b=0.
Generally, a relation is just a collection of
A relation is a collection of ordered pairs (x,y) wherein x is related to y.
The inverse of the statement '4x+1=5 when x=1' is 'If 4x+1≠5, then x≠1' .
False
The inverse of the statement 'If I will not drink coffee, then I will drink milk.' is 'If I will not drink coffee then, I will not drink milk.'.
False
he inverse of the statement 'If he loves her, then he will change' is 'If he will not change, then he does not love her'.
False
It is the condition of the statement.
Hypothesis
What is the hypothesis in the statement 'If I will go to church, then it is Sunday.'?
I will go to church
A ball was dropped from the top of a building. The height of the ball x seconds after it was dropped is given by the function f(x)=−9.8x2+200. Determine the range of the function.
Since the height of the ball cannot be a negative number, the range of the function is 0≤y≤200.
Determine whether the following statement is always, sometimes, or never true:If an if-then statement is true, its inverse will also be true.
Sometimes
Which is true about the converse of an if-then statement.
The converse is obtained by switching the hypothesis and the conclusion.
mapping diagram
The figure formed from the circles and arrow
Which of the following defines a function wherein the y value is obtained by adding 3 to each value of x?
The function f(x)=x+3 defines an equation wherein the corresponding value of y is obtained by adding 3 to a specified value of x.
Choose which is true about the contrapositive of an if-then statement.
The hypothesis and conclusion of the initial statement are switched, and both are negated
The parking fee in mall parking lots is described by the function f(x)=45x where x is the number of hours. Determine the range of the function if you are only allowed to park for a maximum of 1 day.
he range of the function is 0≤y≤1080.
R = {(1, -1), (2, 3), (-2, 4), (4, 6)} Determine whether the following relation R is a function?
here are no ordered pairs that contain the same value of x. Therefore, the relation is a function.
The vertical line test
if a vertical line crosses the graph at more than one point, then the relation is not a function
the system does not have a solution
if there is no intersection
The solutions to linear inequalities are
infinite number of points
The graph of a linear function
is a line with slope , x-intercept , and y-intercept .
What is the conclusion in the statement 'If an animal is a bird, then it has feathers.'?
it has feathers
How to determine if a point is a solution to the system
it should satisfy all of the inequalities in the system. We substitute the point into the linear inequalities.
it is often essential to express a situation in terms of a functional
mathematical model
inverse of an if-then statement
negation of both the hypothesis and the conclusion
How do we formally define a function as a set of ordered pair (x,y)?
no two distinct pairs have the same first number
