Functions and Models

Question 1

Function

Answer 1

A function (f ) is a rule that assigns each element (x ) in a set “D” exactly one element f (x ) in a set E.

Question 2

Domain

Answer 2

The set “D” of a function.

Question 3

f (x )

Answer 3

The value of “f” at “**x”.

Question 4

Range

Answer 4

The set of all possible values of f (x ) as x varies throughout the domain.

Question 5

Independent Variable

Answer 5

A symbol that represents an arbitruary value in the domain of a function (f ).

Question 6

Dependent Variable

Answer 6

A symbol that represents a number in the range of (f ).

Question 7

The Vertical Line Test

Answer 7

A curve in the xy-plane is the graph of a function of x if and only if no vertical line intersects the curve more than once.

Question 8

Absolute Value

Answer 8

Denoted by |a|, the magnitude of a real number without regards to its sign.

Question 9

Step Function

Answer 9

A function that increases or decreases abruptly from one constant value to another.

Question 10

Even Function

Answer 10

A function f that satisfies f (-x) = f (x), for every number “x” in its domain.

Question 11

Odd function

Answer 11

A function f that satisfies f (-x) = -f (x), for every number “x” in its domain.

Question 12

Linear Function

Answer 12

Functions whose graph is a straight line with the form of

y = f (x) = mx + b

Question 13

Polynomial

Answer 13

An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variables.

P(x) = a_n xⁿ + a_n-1 x^n-1 + … + a₂ x² + a₁ x + a₀

Question 14

Quadratic Function

Answer 14

A polynomial of degree 2 in the form of

P(x) = ax² + bx + c

Question 15

Cubic Function

Answer 15

A polynomial of degree 3 of the form

P(x) = ax³ + bx² + cx + d. (a ≠ 0)

Question 16

Power Function

Answer 16

A function of the form f (x) = x^a , where “a” is a constant.

Question 17

Root Function

Answer 17

A function of the form f (x) = x^1/n = ⁿ√x

Question 18

Reciprocal Function

Answer 18

A function of the form f (x) = x^-1 = 1/x.

Question 19

Rational Function

Answer 19

A ratio of two polynomials of the form f (x) = P(x) / Q(x),

where P and Q are polynomials.

• The domain consists of all values of x, such that Q(x) ≠ 0.

Question 20

Algebraic Function

Answer 20

A function that can be constructed using Algebraic Functios (Such as addition, subtraction, multiplication division, and taking roots) starting with polynomials.

• Any Rational Function is automatically an algebraic function.

Question 21

Trigonometric Functions

Answer 21

A function of an angle, or of an abstract quantity, used in trigonometry, (including the sine, cosine, tangent, cotangent, secant, and cosecant, and their hyperbolic counterparts.)

Question 23

Exponential Functions

Answer 23

A function of the form f (x) = a^x

Question 24

Logarithmic Function

Answer 24

A function of the form f (x) = log_ax and the inverse function of the exponential function.