MATHEMATICS 1Integrated Pathway

CHAPTER 2.6.1

Review:

What is a function?A function relates an input to an output

Like an action is related to a reaction

   "f(x) = ... " is the classic way of writing a function. And there are other ways, as you will see!

NamesFirst, it is useful to give a function a name.

The most common name is "f", but we can have other names like "g" ... or even

"marmalade" if we want. But let's use "f":

We say "f of x equals x squared"

what goes into the function is put inside parentheses () after the name of the function:So f(x) shows us the function is called "f", and

"x" goes inAnd we usually see what a function does with

the input:f(x) = x2 shows us that function "f" takes "x"

and squares it. 

THE "X" IS JUST A PLACE-HOLDER!

Example: with f(x) = x2: an input of 4 becomes an output of 16.

In fact we can write f(4) = 16.

In our example, x = 4 (the input is 4) f(x) = 16

graphs: f(x) is given by the y-axis so f(x) is the fancy name of y

Range and Domain

Range: All possible values of f(x) or y (all possible output), as given by the equation.

Domain: All possible values of x as given by the equation

Spotting a linear, exponential or quadratic function

TO RECOGNIZE IF A FUNCTION IS LINEAR, QUADRATIC (A PARABOLA), OR EXPONENTIAL WITHOUT AN EQUATION OR GRAPH, LOOK AT THE DIFFERENCES OF THE Y-VALUES BETWEEN SUCCESSIVE INTEGRAL X-VALUES

x y

-3 -7

-2 -5

-1 -3

0 -1

1 1

2 3

3 5

Linear Function: A constant difference between the y-values (or a constant rate between x and y values)

x y

-3 9

-2 4

-1 1

0 0

1 1

2 4

3 9

Quadratic Function: first difference is not constant but the 2nd difference is.

x y

-3 5

-2 11

-1 29

0 83

1 245

2 731

3 2189

Exponential Function: the difference between y-values follows a pattern (Here the difference between y-valuesIs multiplied by 3: 11-5=6; 6x3=18 which is the difference between 11 and 29)

ABOUT LINEAR FUNCTIONS & EQUATIONS

if

if

xx

yym

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PRE-ASSESSMENT TIME (HAMMER TIME)

Excursive 1-5https://www.youtube.com/watch?v=x8H2-YZUw40

2.6.1

LINEAR AND EXPONENTIAL RELATIONSHIPSLesson 6: Comparing Functions Pre-Assessment: U2-292 & U2-293