Algebra is the branch of mathematics that satisfies operations' properties and the structures which these operations are defined. A **function** is nothing but a relation
between each input number and **one** output number. Algebra functions include exponential function, log function, Quadratic functions, Even and Odd functions. Let us learn some
concepts and example problems in algebra functions.

**Exponential function:**

The function *f* given by f(x) = b x , where *b* > 0, *b `!=`* 1, and the exponent *x* is any real number, is called an
exponential function.

**Log Function:**

The logarithmic function that contain base *b*, where *b* > 0 and *b* `!=` 1, is given by log_{b} and is defined by y =
log_{b} x, if and only if b^{y = x}

^{ }

**Quadratic functions:**

It is a polynomial of highest power two. The basic function is: F(X) = ax^{2} + bx + c. Here ax^{2} is *quadratic term*, bx is *linear term* and c is constant.
The letters a and b are coefficients.

**Even functions**:

The function is called even if the graph is symmetric to y-axis, in other words f(x) = f(- x).

**Odd functions:**

The function is called odd if the graph is symmetric to origin, in other words f(-x) = - f(x).

college algebra functions-Example Problems:

**Sum of functions:**

(f + g)(x) = f(x) + g(x)

**Example 1:**

If f(x) = 4x + 1 and g(x) = x + 2 then find (f + g)(x)

**Solution:**

(f + g)(x) = (4x + 1) + (x + 2)

= 4x + 1 + x + 2

**=
5x + 3**

**Product of functions:**

(fg)(x) = f(x)g(x)

**Example 2:**

If f(x) = 4x + 1 and g(x) = x + 2 then find (fg)(x)

**Solution:**

(fg)(x) = (4x + 1)(x + 2)

= 4x^{2} + 8x + x + 2

**= 4x ^{2} + 9x + 2**