GRE - 2

2.9. Graphs of functions

The coordinate plane can be used for graphing functions. To graph a function in the xy-plane, you represent each input x and its corresponding output f(x) as a point (x,y) where y = f(x). In other words, you use the x-axis for the input and the y-axis for the output. Below are several examples of […]

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2.8. Coordinate geometry

Two real number lines that are perpendicular to each other and that intersect at their respective zero points define a rectangular coordinate system, often called the xy-coordinate system or xy–plane. The horizontal number line is called the x-axis and the vertical number line is called the y-axis. The point where the two axes intersect is called the origin, […]

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2.7. Applications

Translating verbal descriptions into algebraic expressions is an essential initial step in solving word problems. Three examples of verbal descriptions and their translations are given below. Example 2.7.1: If the square of the number x is multiplied by 3 and then 10 is added to that product, the result can be represented algebraically by 3×2 + […]

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2.6. Functions

An algebraic expression in one variable can be used to define a function of that variable. Functions are usually denoted by letters such as f, g, and h. For example, the algebraic expression 3x+5 can be used to define a function f by ƒ(x) = 3x + 5 where ƒ(x) is called the value of ƒ at x and […]

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2.5. Solving linear inequalities

A mathematical statement that uses one of the following four inequality signs is called an inequality. < less than > greater than ≤ less than or equal to ≥ greater than or equal to Inequalities can involve variables and are similar to equations, except that the two sides are related by one of the inequality signs […]

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2.4. Solving quadratic equations

A quadratic equation in the variable x is an equation that can be written in the form ax2 + bx + c = 0 where a, b, and c are real numbers and a≠0. Quadratic equations have zero, one, or two real solutions. The Quadratic Formula One way to find solutions of a quadratic equation is to […]

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2.3. Solving linear equations

An equation is a statement of equality between two mathematical expressions. If an equation involves one or more variables, the values of the variables that make the equation true are called the solutions of the equation. To solve an equation means to find the values of the variables that make the equation true, that is, […]

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2.2. Rules of exponents

In the algebraic expression , where x is raised to the power a, x is called the base and a is called the exponent. For all integers a and b and all positive numbers x, except x = 1, the following property holds: If, xa = xb, then a = b Example: If 23c+1 = 210, then 3c +1 = 10, and therefore, c =  3. Here are seven basic rules […]

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2.1. Algebraic expressions

A variable is a letter that represents a quantity whose value is unknown. The letters x and y are often used as variables, although any symbol can be used. An algebraic expression has one or more variables and can be written as a single term or as a sum of terms. Here are four examples […]

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