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Questions and Answers
What is the domain and range of the function y = 3x?
What is the domain and range of the function y = 3x?
What is the set of all possible x-values that will make a function valid?
What is the set of all possible x-values that will make a function valid?
What defines a relationship between a set of inputs and outputs in mathematics?
What defines a relationship between a set of inputs and outputs in mathematics?
What is the equation representing a total cost of a dozen short pants and half a dozen pajamas at least Php 960?
What is the equation representing a total cost of a dozen short pants and half a dozen pajamas at least Php 960?
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Who is credited with founding the Cartesian Coordinate Plane?
Who is credited with founding the Cartesian Coordinate Plane?
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What term describes the horizontal line in the rectangular coordinate system?
What term describes the horizontal line in the rectangular coordinate system?
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Which symbol differentiates linear equations from linear inequalities?
Which symbol differentiates linear equations from linear inequalities?
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Which of the following is not considered a linear inequality in two variables?
Which of the following is not considered a linear inequality in two variables?
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What is the square of 49?
What is the square of 49?
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Which of the following is not the standard form of a linear inequality?
Which of the following is not the standard form of a linear inequality?
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Study Notes
Domain and Range of a Function
- The domain of a function is the set of all possible input values (x-values) that will produce a real output (y-value).
- The range of a function is the set of all possible output values (y-values) that result from the input values (x-values).
Function Definition
- A function is a relationship between an input (x-value) and an output (y-value). A function assigns exactly one output value to each input value.
- Sets of inputs (x-values) and outputs (y-values) are often written as ordered pairs or can be illustrated by a mapping diagram.
Cartesian Coordinate Plane
- Rene Descartes developed the Cartesian coordinate system.
- The coordinate system is a two-dimensional plane formed by two perpendicular number lines, the x-axis and the y-axis.
- The point of intersection between the two axes is called the origin.
Linear Equations vs. Linear Inequalities
- The symbol
=is used for linear equations. - The symbols
>,<,≥, and≤are used for linear inequalities. - A linear equation represents a straight line on a graph.
- A linear inequality represents a region on a graph, often with a boundary line.
Solving Linear Inequalities
- The key to solving inequality equations rests on the fact that inequalities follow similar rules as equations, with one exception: when an inequality is multiplied or divided by a negative number, the inequality sign must be reversed.
Linear Function vs. Non-linear Function
- Linear functions are represented as y = mx + b, where m is the slope and b is the y-intercept.
- Non-linear functions have a relationship that isn't a straight line and don't follow the form of ax + b.
Problem-Specific Information
- A dozen short pants (s) added to half a dozen of pajamas (p) has a total cost greater than or equal to Php 960 can be expressed as 12p + 6s ≥ 960.
- The square of 49 is 2,401.
- The square of 16 is 256.
- One of the symbols that is not used in linear inequalities is the equal symbol.
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Description
This quiz covers the fundamental concepts of functions, including domain and range, as well as the Cartesian coordinate plane. You'll learn how functions are defined and the differences between linear equations and inequalities. Test your understanding of these essential mathematical principles!
