15 Questions
What is the correct mathematical statement for 'The total amount of 5 Peso and 10 Peso coins in Kyle’s bag is more than PHP 300'?
$5a + 10b > 300$
What is the correct mathematical statement for 'The sum of 20-peso bills (t) and 50-peso bills (f) that Vienne has is greater than 500'?
$20t + 50f > 500$
What is the cost of a tray of medium-sized eggs if Euricka paid at least Php 550 for a tray of extra-large sized eggs and 2 trays of medium-sized eggs, given that a tray of XL sized eggs costs 204?
$104$
In the given context, what does the term 'domain' refer to?
The x-values or first elements in the relation
What is the solution type when a system of linear inequalities forms a common shaded region bounded by 3 lines?
Closed or bounded solution
What does the term 'range' refer to in the context of relations and functions?
The y-values or second elements in the relation
What is represented by the shaded area in the graph of a linear inequality?
The solution of the inequality represented by the shaded half-plane
When is a system of linear inequalities considered to have an open or unbounded solution?
When there are many solutions on both sides of the line
What is a relation in terms of sets of ordered pairs?
Any pairing of elements of two sets
Which type of relation involves no two pairs having the same first element (x-values)?
One-To-One Relation
In the context of functions, what does the term 'domain' refer to?
The set of input values (x-values) of the function
What is the correct evaluation of f(2) if f(x) = x^2 - 3x + 2?
$f(2) = 4$
For the function h(x) = 5x - 3, find the value of x for which h(x) = 12.
$x = 3$
What is the type of relation where multiple x-values correspond to a single y-value?
Many-To-One Relation
In the context of relations and functions, what does the term 'range' refer to?
The set of output values (y-values) of the function
Study Notes
Inequalities and Functions
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The total amount of 5 Peso and 10 Peso coins in Kyle's bag can be mathematically represented as 5x + 10y > 300, where x and y are the number of coins.
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The sum of 20-peso bills (t) and 50-peso bills (f) that Vienne has can be mathematically represented as 20t + 50f > 500.
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The cost of a tray of medium-sized eggs, if Euricka paid at least Php 550 for a tray of extra-large sized eggs and 2 trays of medium-sized eggs, is Php 173, since 550 - 204 = 346, and 346 ÷ 2 = 173.
Domain and Range
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In the context of relations and functions, the term 'domain' refers to the set of input values or x-values.
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The term 'range' refers to the set of output values or y-values.
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A relation in terms of sets of ordered pairs is a collection of points on a coordinate plane, where each point is represented as an ordered pair (x, y).
Function Types
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A function involves no two pairs having the same first element (x-values), meaning that each input value has a unique output value.
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A relation where multiple x-values correspond to a single y-value is not a function.
Linear Inequalities
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The shaded area in the graph of a linear inequality represents the solution to the inequality.
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A system of linear inequalities is considered to have an open or unbounded solution when the common shaded region is not bounded by a specific point.
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When a system of linear inequalities forms a common shaded region bounded by 3 lines, the solution type is a polygon.
Function Evaluations
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The correct evaluation of f(2) if f(x) = x^2 - 3x + 2 is f(2) = 2^2 - 3(2) + 2 = 0.
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For the function h(x) = 5x - 3, the value of x for which h(x) = 12 is x = 3, since 5x - 3 = 12, and x = (12 + 3) ÷ 5 = 3.
Test your understanding of linear inequalities and their symbols with this quiz. Practice identifying and solving linear inequalities with various symbols of inequality, including less than, greater than, less than or equal to, and greater than or equal to.
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