1. Vocabulary
Algebra 1

2. 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

3. 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

4. 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

5. 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

6. 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

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

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

9. 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

10. 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

11. 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.

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

13. 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.

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

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

16. 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.
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)

17. 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.

18. 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.

19. 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

20. 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

21. 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)

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