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1.1.3 Examples of functions and their graphs
The graph of a function
The graph of a function is the set of points in the plane of the form (x, y) where x is in the domain of function and also y = f (x).
We discuss some important types of functions and observe their graphs. Pay attention to the manner in which the graphs of these functions. All examples are algebraic functions, we will discuss other types of functions such as trigonometric functions later. For now, observe the following functions and their graphs.
constant function: f (x) = k, where k is some constant

What all have in common the graphics? How do they differ?
linear function: f (x) = ax + b

What have in common the graphics? How do they differ?
quadratic function: f (x) = ax2 + bx + c = a (x - x0) 2 + y0
The red dot is called the vertex of the parabola.
What are your coordinates?
How are the coordinates of the vertices with the numbers in the form f (x) = a (x-x0) 2 + y0?
f (x) = x2 + 2 x + 1 = (x + 1) 2

The red dot is called the vertex of the parabola.
What are your coordinates?
How are the coordinates of the vertices with the numbers in the form f (x) = a (x-x0) 2 + y0?
f (x) = 2 x2 + x = (x + 1) 2 to 1

The red dot is called the vertex of the parabola.
What are your coordinates?
How are the coordinates of the vertices with the numbers in the form f (x) = a (x-x0) 2 + y0?
f (x) = 2 x - x2 = 1 - (x - 1) 2

The red dot is called the vertex of the parabola.
What are your coordinates?
How are the coordinates of the vertices with the numbers in the form f (x) = a (x-x0) 2 + y0?
What significance have the numbers, x0, y0 to the graph of the function f (x) = a (x-x0) 2 + y0?

f (x)
= 10 + 2 x - 2 x2 1
21




= - 2 [- (
) + x2] 2



2


polynomial function P (x) = x3 - 3x2 + 2x - 7
racionalUna function rational function is a quotient of two polynomials, f (x) = P (x) / Q (x) x + 4

f (x) = x2

- 16 What happens in x values \u200b\u200bwhere the denominator equals zero?
Power function: f (x) = k xnEn where k is any real constant and n is a real number.
For now we will restrict ourselves to rational exponents. Functions as xpi will discussed later. The domain of a power function depends on the exponent n.
f (x) = x-1


f (x) = x1 / 3


f (x) = x1 / 2


f (x) = x2 / 3



defined function by sections
is not necessary that a function is defined by a single formula. The matching rule may depend on what part of the domain from the independent variable.
In the following two graphs look at two examples of functions defined in sections.



f (x) = {
x2,
4 x, if 0
<= x <= 5
f (x) = {
-x2,
if x < 0
3,
if 0 <= x < 1
2 x - 1,
if x> = 1