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= + ÷ ± ∆ ∞ × π Σ f(x) % ≤ ! ≠ *

Families of Functions

A function is a relation with a one-to-one correspondence of input and output.

That makes it predictable in that each input only produces one output.

An input is the independent variable: you choose what to put in
An output is the dependent variable: once you choose the input, the output is determined by the relation.

A function family describes the type of function, e.g. lines, parabolas, and absolute value.

Typically it is also easy to identify these by looking at their graphs.

Example: suppose the rule is: "double, then add 5"

some possible inputs: 0, 1, 2, 3 or -1, -2, -3

for 0, output is 0 + 5 = 5

for 1 the output is 2 + 5 = 7

for 2 the output is 4 + 5 = 9

for 3 the output is 6 + 5 = 11

for -1 the output is -2 + 5 = 3

for -2 the output is -4 + 5 = 1

for -3 the output is -6 + 5 = -1

Note: This is an example of a linear function. Its graph is a line.

Example: suppose the rule is: "square, then add 5"

some possible inputs: 0, 1, 2, 3 or -1, -2, -3

for 0, output is 0 + 5 = 5

for 1 the output is 1 + 5 = 6

for 2 the output is 4 + 5 = 9

for 3 the output is 9 + 5 = 14

for -1 the output is 1 + 5 = 6

for -2 the output is 4 + 5 = 9

for -3 the output is 9 + 5 = 14

Note: This is an example of a quadratic function. Its graph is a parabola, sometimes called a "U" graph .

Example: suppose the rule is: "compute the absolute value, then add 5"

some possible inputs: 0, 1, 2, 3 or -1, -2, -3

for 0, output is 0 + 5 = 5

for 1 the output is 1 + 5 = 6

for 2 the output is 2 + 5 = 7

for 3 the output is 3 + 5 = 8

for -1 the output is 1 + 5 = 6

for -2 the output is 2 + 5 = 7

for -3 the output is 3 + 5 = 8

Note: This is an example of an absolute value function. Its graph is a "V" (two rays with a common vertex.)

Now, if you came from the sample questions, let's get back to those (and some I've added)

(you can click on the link for help)

To which family of functions will this equation belong?

	this is a quadratic equation
	this is a linear equation in standard Ax + By = C fprm
	this is an absolute value equation
	this is a linear equation in slope intercept form (the slope is 0)
	this is a linear equation in function notation
	this is a linear equation where the y-intercept is 0 (and therefore not written)

you can see the graphs of these functions by clicking here