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A number's distance from zero on the number line.
The y-coordinate of the vertex of the quadratic function f(x) = ax^2 + bx +c, where a < 0.
A figure is moved from one location to another on the coordinate plane without changing its size, shape, or orientation.
|x|
Functions which map points of a pre-image onto its image.
f(x) = -4x^2 + 12x + 18
For this function, a = -4, so the graph opens down and the function has a maximum value.
A plane divided into four quadrants by the intersection of the x-axis and the y-axis at the origin.
Two functions f and g are inverse functions if and only if both of their compositions are the identity function.
A transformation in which all distances on the coordinate plane are lengthened by multiplying all x-coordinates by a common factor greater than 1.
The set of all x-coordinates of the ordered pairs in a relation.
A mathematical sentence stating that two mathematical expressions are equal.
2x+3
(y-3)/2
The domain of the relation (0, 1),(1, 2),(1, 3),(4, 6) is x=0, 1, 4.
n + 15 = 91
A point at which a function is not continuous or is undefined, and cannot be made continuous by being given a new value at the point.
Conditions given to variables, often expressed as linear inequalities.
From the graph of y = f(x), the graph of
y = f(cx) is a horizontal compression if c > 1, horizontal stretch if c < 1.
A function that is not continuous at a point in its domain.
A function which for certain values or between certain values of the variable does not vary continuously as the variable increases.
A store has requested a manufacturer to produce pants and sports jackets. For materials, the manufacturer has 750 m^2 of cotton textile and 1,000 m^2 of polyester. Every pair of pants (1 unit) needs 1 m2 of cotton and 2 m^2 of polyester. Every jacket needs 1.5 m^2 of cotton and 1 m^2 of polyester. The price of the pants is fixed at $50 and the jacket, $40. What is the number of pants and jackets that the manufacturer must give to the stores so that these items obtain a maximum sale?
The set of all y-coordinates in a relation.
A replacement for the variable in an open sentence that results in a true sentence.
The range of the relation (0, 1),(1, 2),(1, 3),(4, 6) is y=1, 2, 3, 6.
x = 12
A function whose ordered pairs satisfy a linear equation.
A function that is written using two or more expressions.
An algebraic expression made up of one or more terms.
Any of the points of intersection of the graphs of the constraints that determine a feasible region.
The coefficient of the term with the highest degree.
The behavior of the graph as x approaches positive infinity or negative infinity.
{
f(x) = x-2 if x < -1
x+3 if x > -1
The number or quantity whose cube is a given number or quantity.
y = 2x^3 + x^2 + 9
A function described by the equation f(x) = ax^2 + bx +c, where a is not equal to 0.
Even, positive
2 is the cube root of 8
The y-coordinate of the vertex of the quadratic function f(x) = ax^2 + bx +c, where a > 0.
A point on the graph of a function where no nearby points have a greater/lesser y-coordinate.
A relation that holds between two values when they are different.
Calculation by mathematical methods.
A number that produces a specified quantity when multiplied by itself.
2x + 12 > 7
The four basic arithmetic operations are addition, subtraction, multiplication, and division.
A transformation in which all distances on the coordinate plane are lengthened by multiplying all y-coordinates by a common factor greater than 1.
2 x 2 = 4
2^2 = 4
The square root of 4 is 2.
f(x) = 3x^2 + 12x + 18
For this function, a = 3, so the graph opens down and the function has a minimum value.
The x-intercepts of the graph of a function; the points for which f(x) = 0.
The vertical dilation for the function y = x^2 with the scale factor 3.
y = x^2
After dilation:
Y= 3x^2