12.1 functions

Copy planner

functions

• Functions are basically the same as equations, they are just written differently.

• F(x) means the function of “x” – What value of “x” to use

• Y = 2x – 4 (equation)• F(x) = 2x – 4 (function)• Instead of have a “y” value, you use the f(x) to

show what the function would equal with a specific value.

function

• A function of “x” is a relationship in which no 2 ordered pairs have the same x-value

• 3 types of functions to recognize– Linear function– Quadratic function – Exponential function

• A graph that is not a function will have “x” values that are the same

Domain & range

• Domain: all x-values that can be input into a function.

• Range: the y-values or the “output” of the functions

• Function or not a function(1,6) (3,6) (3,7) (8,9)(1,6) (2,6) (3,7) (8,9)

Evaluating a function

• F(x) = 2x – 3• X = -2• Input -2 everywhere there is an “x”• F(-2) = 2(-2) – 3• F(-2) = -7• F(0) =• F(0) = -3

Real life functions

• Functions are often used by companies to determine how to price their products.

• X = cost of materials• Pricing function f(x) = 2x + 10• X = 8• F(8) = 2(8) +10• F(8) = $26• So, if the business spends $8 to make an item,

they would charge a customer $26 to buy it.

review

• What can a function NOT have?• No 2 ordered pairs w/the same x-value• What is the domain?• X-values• What is the range?• Y-values

12.2 linear functions

• Linear function in slope-intercept form: • F(x) = mx + b• To write an ordered pair in function notation• f(-2) = 4 is the same as (2, -4)

Linear functions

• Find a function for f(2) = 5 and f(6) = 3• Remember, this is the same as having 2 points (2,5) and

(6,3)• Find the slope• M = -1/2• Substitute the slope into the function & 1 of the point

to solve for the y-intercept, b• What is the function?• F(x) = -1/2(x) + 6• When in doubt, treat like a regular equation

Let’s try some