College Algebra Final Exam 2023

College Algebra Final Exam 2023 Absolute value - ANSWER The distance from 0 to n on the number line |n|= n when n>=0 and -n when n<0 Algebraic expression - ANSWER An expression containing numbers, operation signs, and variables such as 4x-3y/2z Arithmetic expression - ANSWER An expression containing numbers and operation signs, such as 7+3(-2)/2 A systyem of equations - ANSWER Two or more equations considered together. Arithmetic sequence - ANSWER A sequence where the difference between two consecutive terms is a fixed number Arithmetic series - ANSWER The indicated sum of an arithmetic sequence. Asymptote - ANSWER A straight line that a curve will approach but never touch. Augmented matrix - ANSWER A matrix consisting of the coefficients of the variables and the constants in a system of equations. Base change formula - ANSWER a, b, and x are positive numbers. Complex number - ANSWER A number that can be written in the form a + bi, where a and b are real numbers. Conjugate - ANSWER The conjugate of a + bi is a - bi. Constant function - ANSWER A function f(x) = c, where c is a real number that does not change according to x variables and its graph is a line. Coordinate formula for slope - ANSWER The slope of the line through (x1,y1) and (x2,y2) is given by m= y2-y1/x2-x1, provided that x2-x1 does not = 0 Cube root - ANSWER The cube root of a number x is denoted by ^3Sqrt(x) whose cube is x. x=^3Sqrt(x)^3 Cubing function - ANSWER A function of the form f(x)=ax^3+bx^2+d where a does not =0 Common difference - ANSWER This occurs when the difference between two consecutive terms of a sequence is a fixed number. Common logarithm - ANSWER The logarithm to base 10. Common ratio - ANSWER This occurs if the ratio between two consecutive terms of a sequence is a fixed number Complex fraction - ANSWER A fraction that has other fractions in the numerator, denominator, or both. Consistent equations - ANSWER The graphs of the equations intersect at one point, whose coordinates give the solution of the system. Also known as independent equations. Degree - ANSWER The highest power of x. Discriminant - ANSWER The expression b^2-4ac under the radical in the quadratic formula is called the discriminant. Domain - ANSWER The set of all possible values of an independent variable, x, of a function, f(x). Decreasing function - ANSWER A function whose graph falls from left to right. Dependent equations - ANSWER The graphs of the equations coincide (are the same). There are infinitely many solutions for the system. Dependent system - ANSWER A system in which both equations are equivalent. Double root - ANSWER A root of an equation that comes from two factors. Exponential function - ANSWER A function defined for all real values of x by f(x)=b^x, b>0, b does not = 1 Expression - ANSWER A collection of numbers and letters connected by operation signs, such as x+y^3z Elimination method - ANSWER A method used to solve systems of equations by multiplying by numbers that cause the coefficients of one of the variables to be opposites. Equation - ANSWER A statement that two algebraic expressions are equal Evaluate - ANSWER To substitute a value with one or more of the variables in an expression. Exponent - ANSWER Power of a number that indicates the number of times a quantity is multiplied by itself.