Vocabulary Algebra 1

A relation that assigns exactly one value in the range to each value of the domain. Function Earned income is a function of the number of hours worked. If you earn $4.50/h, then your income is expressed by the function f(h) = 4.5h. Function Not a Function

A variable that provides the input values of a function. Independent quantity In the equation y = 3x, x is the independent variable. x y 1 3 2 6 9

Dependent quantity A variable that provides the output values of a function. In the equation y = 3x, the value of y depends upon the value of x. x y 1 3 2 6 9

Domain In the function f(x) = x + 22, the domain is all real numbers. The possible values for the input, or the independent variable, of a function. Domain In the function f(x) = x + 22, the domain is all real numbers. x f(x) -5 18 22 10.5 32.5

The possible values for the output, or dependent variable, of a function. Range In the function y = x2, the range is the set of all nonnegative numbers. x y -5 25 7 49

Data where numbers between any two data values have meaning. Continuous Temperature, length, or weight

Discrete Data that involve a count of items. Number of people or number of cars

The x- or y- coordinate of the point where a line crosses the x- or y- axis. Intercepts (x- and y-) The x-intercept of 3x + 4y = 12 is 4. The y-intercept of y = 5x + 2 is 2. y-intercept x-intercept

Linear An equation or function whose graph forms a straight line. The graph of y = 2x + 5 is linear. y = x2 – 3 is not linear. Linear Non-linear

Parent function The linear parent function is y = x. A family of functions is a group of functions with common characteristics. A parent function is the simplest function with these characteristics. Parent function Linear Parent Function Quadratic Parent Function The linear parent function is y = x. The quadratic parent function is y = x2.

Slope The ratio of the vertical change to the horizontal change. The slope of the line graphed is

A linear equation of a nonvertical line written as y = mx + b, where m is the slope and b is the y- intercept. Slope-intercept form In the equation y = 3x + 2, the slope of the graph of the line is 3 and the y-intercept is 2.

A mathematical sentence that compares the values of two expressions using an inequality symbol. -3 -2 -1 1 2 3

System of equations Two or more equations using the same variables. The graph represents the system

x2 – 4 = (x – 2)(x + 2) Factor (polynomials) A factor of polynomial P(x) is any polynomial which divides evenly into P(x). The factorization of a polynomial is its representation as a product its factors. www.mathwords.com Factor (polynomials) For example, x + 2 is a factor of the polynomial x2 – 4. For example, the factorization of x2 – 4 is (x – 2)(x + 2). x2 – 4 = (x – 2)(x + 2)

The resulting graph of a function when the function’s parameters are changed. changes The graph shows the function f(x) = x2 and f(x) = x2 – 3. The parabola shifted down 3 units.

Polynomial Polynomial A monomial or the sum or difference of two or more monomials. A quotient with a variable in the denominator is not a polynomial. Polynomial Not Polynomial Polynomial 2x2, 3x + 7, 28, and – 7x3 – 2 x2 + 9 are all polynomials.

Quadratic function y = 2x2 + 3x + 1 A function of the form y = ax2 + bx + c, where a = 0. The graph of a quadratic function is a parabola, a U-shaped curve that opens up or down. Quadratic function y = 2x2 + 3x + 1

An equation you can write in the standard form ax2 + bx + c = 0. A quadratic equation can have two, one or no real solutions. Quadratic equation

Vertex The vertex of the parabola is located at (0 , – 4) The highest or lowest point on a parabola. The axes of symmetry intersects the parabola at the vertex Vertex The vertex of the parabola is located at (0 , – 4)

Zeroes (solutions) The x-intercepts of the graph of a function. The zeroes of the function are (-3 , 0) and (3 , 0).