# How to solve by graphing

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## How can we solve by graphing

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College algebra is the study of equations and functions. A function is a mathematical relationship between two variables, usually represented by an equation. College algebra functions are used to model real-world situations. For example, a function can be used to model the relationship between the amount of money you earn and the number of hours you work. College algebra functions can be linear or nonlinear. Linear functions have a constant rate of change, while nonlinear functions have a variable rate of change. College algebra functions can also be continuous or discontinuous. Continuous functions are smooth, while discontinuous functions have breaks or gaps. College algebra functions can be graphed on a coordinate plane. The x-axis is the independent variable and the y-axis is the dependent variable. The graph of a function can give you information about the function, such as its domain and range. College algebra is a important tool for solving real-world problems. Functions can be used to model relationships in business, science, and engineering. College algebra is also the foundation for calculus, which is used in physics and other sciences.

Absolute value is a concept in mathematics that refers to the distance of a number from zero on a number line. The absolute value of a number can be thought of as its magnitude, or how far it is from zero. For example, the absolute value of 5 is 5, because it is five units away from zero on the number line. The absolute value of -5 is also 5, because it is also five units away from zero, but in the opposite direction. Absolute value can be represented using the symbol "| |", as in "|5| = 5". There are a number of ways to solve problems involving absolute value. One common method is to split the problem into two cases, one for when the number is positive and one for when the number is negative. For example, consider the problem "find the absolute value of -3". This can be split into two cases: when -3 is positive, and when -3 is negative. In the first case, we have "|-3| = 3" (because 3 is three units away from zero on the number line). In the second case, we have "|-3| = -3" (because -3 is three units away from zero in the opposite direction). Thus, the solution to this problem is "|-3| = 3 or |-3| = -3". Another way to solve problems involving absolute value is to use what is known as the "distance formula". This formula allows us to calculate the distance between any two points on a number line. For our purposes, we can think of the two points as being 0 and the number whose absolute value we are trying to find. Using this formula, we can say that "the absolute value of a number x is equal to the distance between 0 and x on a number line". For example, if we want to find the absolute value of 4, we would take 4 units away from 0 on a number line (4 - 0 = 4), which tells us that "the absolute value of 4 is equal to 4". Similarly, if we want to find the absolute value of -5, we would take 5 units away from 0 in the opposite direction (-5 - 0 = -5), which tells us that "the absolute value of -5 is equal to 5". Thus, using the distance formula provides another way to solve problems involving absolute value.

A radical is a square root or any other root. The number underneath the radical sign is called the radicand. In order to solve a radical, you must find the number that when multiplied by itself produces the radicand. This is called the principal square root and it is always positive. For example, the square root of 16 is 4 because 4 times 4 equals 16. The symbol for square root is . To find other roots, you use division. For example, the third root of 64 is 4 because 4 times 4 times 4 equals 64. The symbol for the third root is . Sometimes, you will see radicals that cannot be simplified further. These are called irrational numbers and they cannot be expressed as a whole number or a fraction. An example of an irrational number is . Although radicals can seem daunting at first, with a little practice, they can be easily solved!

Algebra is the branch of mathematics that deals with the solution of equations. In an equation, the unknown quantity is represented by a letter, usually x. The object of algebra is to find the value of x that will make the equation true. For example, in the equation 2x + 3 = 7, the value of x that makes the equation true is 2. To solve an equation, one must first understand what each term in the equation represents. In the equation 2x + 3 = 7, the term 2x represents twice the value of x; in other words, it represents two times whatever number is assigned to x. The term 3 represents three units, nothing more and nothing less. The equal sign (=) means that what follows on the left-hand side of the sign is equal to what follows on the right-hand side. Therefore, in this equation, 2x + 3 is equal to 7. To solve for x, one must determine what value of x will make 2x + 3 equal to 7. In this case, the answer is 2; therefore, x = 2.

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