**Exponential functions**follow all the

**rules**of

**functions**. The parent

**exponential function**f(x) = b

^{x}always has a horizontal asymptote at y = 0, except when b = 1. You can't raise a positive number to any power and get 0 or a negative number.

So, what is an exponential function in math?

An

**exponential function**is a mathematical**function**of the following form: f ( x ) = a^{x}. where x is a variable, and a is a constant called the base of the**function**. The most commonly encountered**exponential**-**function**base is the transcendental number e , which is equal to approximately 2.71828.1

## What are the rules of exponents?

A Review of the Rules for Exponents. Below is List of Rules for Exponents and an

**example**or two of using each rule: Zero-Exponent Rule: a^{0}= 1, this says that anything raised to the zero power is 1.**Power Rule**(Powers to Powers): (a^{m})^{n}= a^{mn}, this says that to raise a power to a power you need to**multiply**the exponents2

## What is the initial value of the exponential function?

For an

**exponential function**the y-intercept is the "**initial value**" not the common ratio. Consider a standard**exponential function**of the form y(x) = a•rˣ , if you put in x = 0 you get: y(0) = a•rˣ = a•r° = a•1 = a , so the y-intercept is a , which is called the**initial value**, not r , which is called the common ratio.3

## What is the base of the exponential function?

The

**function**f(x)=3x is an**exponential function**; the variable is the**exponent**. If f(x) = ax, then we call a the**base**of the**exponential function**. The**base**must always be positive. In fact, for any real number x, 1x = 1, so f(x)=1x is the same**function**as the constant**function**f(x) = 1.4

## What is an exponential graph?

**Graphs**of

**Exponential**Functions. The

**graph**of y=2

^{x}is shown to the right. Here are some properties of the

**exponential**function when the base is greater than 1. The

**graph**passes through the point (0,1) The domain is all real numbers.

5

## Can a be negative in an exponential function?

The base b in an

**exponential function**must be positive. Because we only work with positive bases, b^{x}is always positive. The values of f(x) , therefore, are either always positive or always**negative**, depending on the sign of a .**Exponential functions**live entirely on one side or the other of the x-axis.6

## Can the base of an exponential function be zero?

1. The graph neither increases nor decreases as ? ∞ because it is a constant

**function**. Using**0**as a**base**for an**exponential function would**be undefined for**negative**values of . As shown in the graph in Focus 2, the domain of / =**0**is only defined in the interval (**0**,∞).7

## Are cubics polynomials?

A

**cubic polynomial**is a**polynomial**of degree 3. A univariate**cubic polynomial**has the form . An equation involving a**cubic polynomial**is called a**cubic**equation. A closed-form solution known as the**cubic**formula exists for the solutions of an arbitrary**cubic**equation.8

## What is exponent law?

The

**exponent laws**, also called the**laws**of indices (Higgens 1998) or power**rules**(Derbyshire 2004, p. 65), are the**rules**governing the combination of**exponents**(powers). The**laws**are given by. (1)9

## What is a polynomial function?

A

**polynomial function is**a**function**such as a quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of x. We can give a general defintion of a**polynomial**, and define its degree. 2.**What is**a**polynomial**?10

## What does an exponential function look like?

**Exponential**Functions. If you think of functions with exponents, you're probably used to seeing something

**like**this. That's the graph of y = x2, and it is indeed a function with an exponent. In an

**exponential**function, the independent variable, or x-value,

**is the**exponent, while the base is a constant.

11

## Are lines polynomials?

The graph of a first degree

**polynomial**is always a straight**line**. The graph of a second degree**polynomial**is a curve known as a parabola. A**polynomial**of the third degree has the form shown on the right.12

## How many terms are there in a polynomial?

Polynomials can be classified by the number of terms with nonzero coefficients, so that a one-term polynomial is called a monomial, a two-term polynomial is called a binomial, and a three-term polynomial is called a trinomial. The term "quadrinomial" is occasionally used for a

**four**-term polynomial.13

## What is a second degree polynomial?

In algebra, a quadratic

**function**, a quadratic**polynomial**, a**polynomial**of**degree**2, or simply a quadratic, is a**polynomial function**in one or more variables in which the highest-**degree**term is of the**second degree**.14

## Is a polynomial?

**Polynomials**.

**Polynomials**in one variable are algebraic expressions that consist of terms in the form where n is a non-negative (i.e. positive or zero) integer and a is a real number and is called the coefficient of the term. The degree of a

**polynomial**in one variable is the largest exponent in the

**polynomial**.

15

## What is the quadratic formula?

In elementary algebra, the

**quadratic formula**is the solution of the**quadratic equation**. There are other ways to**solve**the**quadratic equation**instead of using the**quadratic formula**, such as factoring, completing the square, or graphing.16

## What is the definition of the quadratic formula?

**Quadratic Formula**. The

**quadratic formula**, , is used in algebra to solve

**quadratic equations**(polynomial

**equations**of the second degree). The general form of a

**quadratic equation**is , where x represents a variable, and a, b, and c are constants, with . A

**quadratic equation**has two solutions, called roots.

17

## What are quadratic equations used for?

Quadratic equations are also used when gravity is involved, such as the path of a ball or the

**shape**of cables in a suspension bridge. A very common and easy-to-understand application of a quadratic function is the trajectory followed by objects thrown upward at an angle.18

## What is the quadratic formula and what is it used for?

While

**factoring**may not always be successful, the Quadratic Formula can always find the solution. The Quadratic Formula uses the "a", "b", and "c" from "ax^{2}+ bx + c", where "a", "b", and "c" are just numbers; they are the "**numerical**coefficients" of the quadratic equation they'**ve**given you to solve.