Vocabulary

Algebra 1

Function Not a Function

FunctionA relation that assigns exactly one value in the range to each value of the domain.

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.

Independent quantity

A variable that provides the input values of a function.

x y1 32 63 9

In the equation y = 3x, x is the independent variable.

Dependent quantity

A variable that provides the output values of a function.

x y1 32 63 9

In the equation y = 3x, the value of y depends upon the value of x.

DomainThe possible values for the input, or the independent variable, of a function.

x f(x)-5 180 22

10.5 32.5

In the function f(x) = x + 22, the domain is all real numbers.

RangeThe possible values for the output, or dependent variable, of a function.

x y-5 250 07 49

In the function y = x2, the range is the set of all nonnegative numbers.

Continuous

Data where numbers between any two data values have meaning.

Temperature, length, or weight

Discrete Data that involve a count of items.

Number of people or number of cars

Intercepts (x- and y-)

The x- or y- coordinate of the point where a line crosses the x- or y- axis.

The x-intercept of 3x + 4y = 12 is 4. The y-intercept of y = 5x + 2 is 2.

y-intercept

x-intercept

Linear Non-linear

LinearAn equation or function whose graph forms a straight line.

The graph of y = 2x + 5 is linear.The graph of y = x2 – 3 is not linear.

Parent function

A family of functions is a group of functions with common characteristics. A parent function is the simplest function with these characteristics.

The linear parent function is y = x.The quadratic parent function is y = x2.

Linear Parent Function

Quadratic Parent Function

SlopeThe ratio of the vertical change to the horizontal change.

The slope of the line graphed is 1

2 yx

xy

Slope-intercept form

A linear equation of a nonvertical line written as y = mx + b, where m is the slope and b is the y- intercept.

In the equation y = 3x + 2, the slope of the graph of the line is 3 and the y-intercept is 2.

-3 -2 -1 0 1 2 3

InequalityA mathematical sentence that compares the values of two expressions using an inequality symbol.

x > 1

System of equations

Two or more equations using the same variables.

1

21

22

y x

y x

The graph represents the system

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

x2 – 4 = (x – 2)(x + 2)

For example, x + 2 is a factor of the polynomial x2 – 4.For example, the factorization of x2 – 4 is (x – 2)(x + 2).

Parameter changes

The resulting graph of a function when the function’s parameters are changed.

The graph shows the function f(x) = x2 and f(x) = x2 – 3.The parabola shifted down 3 units.

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.

Not Polynomial

3 22 9x x x

2

24 5x

x

Polynomial 2x2, 3x + 7, 28, and – 7x3 – 2 x2 + 9 are all polynomials.

Quadraticfunction

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.

y = 2x2 + 3x + 1

2 9 0

( 3)( 3) 0

3 0 3 0

3 3

x

x x

x or x

x or x

Quadraticequation

An equation you can write in the standard form ax2 + bx + c = 0.

A quadratic equation can have two, one or no real solutions.

2 0 ax bx c

VertexThe highest or lowest point on a parabola. The axes of symmetry intersects the parabola at the 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).