Introduction to Linear Relations and Functions
Do Now: The following table contains measurement of temperature in Celsius ( C ) and
Fahrenheit ( F ).
C
F=
0
32
5
41
10
50
15
59
20
68
1. Plot the given data from the chart.
2. Based on the scatter plot sketched above, describe the relation between C and F.
3. Write an equation to express relation C and F.
25
77
Definition of a Linear Function
Examples of linear functions
General graphs of linear functions
( special lines – vertical and horizontal lines )
Domain and Range
Definition of function
Definition of a one–to–one function
Notation of functions
f ( x)  2 x  3
g (a )  .5a  5
2
1
h( k )  k 
5
2
Note: f(x), g(a), and h(k) are called the dependent variables whose independent variables are x,
a, and k respectively.
Inverse of linear functions
1. Algebraic definition:
2. Graphic definition:
3.
Examples of inverse notation:
f 1  x 
y 1
g 1  x 
Class work
1. Determine whether each of following is a linear function.
a. f ( x)  3x  4
b. g ( x)  x  3  5
d . h( x )  x 2  3 x
e. f ( x)  6
f.
c. y 
x
6
y
x
5
g. x  6
2. Complete the table below.
Equations
y
Domain
Range
Is it a
functions
Is it a oneto-one
function
2
x6
3
f  x   2( x  2)
g ( x )  3
x2
3. Write an equation of the inverse for each.
a ) y  5 x  3
b) f ( x ) 
1
x 3
2
c) 2 x  y  6
4. Write the equation of the line passing through points ( -5, 2 ), ( 4, 10 ).
Is the inverse
a function
Homework
1. Determine whether each of following is a linear function.
a. f ( x)  .2 x  5
d . h( x ) 
1 2
x  8x
2
b. x  5
e. 3 y  7  2 x
x
2
x
f.
 4
y
c. y 
g . y  2
2. Complete the following table.
Equations
y
Domain
Range
Is it a
functions
Is it a oneto-one
function
1
x2
5
f  x   5
g ( x) 
x
6
x  5
3. Write the equation of the inverse for each.
a) y  7 x  2
b)  x  3 y  9
c) f ( x) 
2
x 5
3
4. Write the equation of the line passing through points ( 3, 0 ), ( -1, 6 ).
Is the inverse
a function