0'2

1
0.2
Some Important Functions
2
Section Outline

• Linear Equations
• Applications of Linear Functions
• Piece-Wise Functions
• Quadratic Functions
• Polynomial Functions
• Rational Functions
• Power Functions
• Absolute Value Function

3
Linear Equations
4
Linear Equations
CONTINUED
5
Applications of Linear Functions
EXAMPLE

• (Enzyme Kinetics) In biochemistry, such as in the
  study of enzyme kinetics, one encounters a linear
  function of the form
  , where K and V are constants.
• If f (x) 0.2x 50, find K and V so that f
  (x) may be written in the form,
  .
• Find the x-intercept and y-intercept of the
  line in terms
  of K and V.

SOLUTION
(a) Since the number 50 in the equation f (x)
0.2x 50 is in place of the term 1/V (from the
original function), we know the following.
Explained above.
50 1/V
Multiply both sides by V.
50V 1
Divide both sides by 50.
V 0.02
Now that we know what V is, we can determine K.
Since the number 0.2 in the equation
f (x) 0.2x 50 is in place of K/V (from the
original function), we know the following.
6
Applications of Linear Functions
CONTINUED
Explained above.
0.2 K/V
0.2V K
Multiply both sides by V.
Replace V with 0.02.
0.2(0.02) K
Multiply.
0.004 K
Therefore, in the equation f (x) 0.2x 50, K
0.004 and V 0.02.
(b) To find the x-intercept of the original
function, replace f (x) with 0.
This is the original function.
Replace f (x) with 0.
Solve for x by first subtracting 1/V from both
sides.
7
Applications of Linear Functions
CONTINUED
Multiply both sides by V/K.
Simplify.
Therefore, the x-intercept is -1/K. To find the
y-intercept of the original function, we
recognize that this equation is in the form y
mx b. Therefore we know that 1/V is the
y-intercept.
8
Piece-Wise Functions
EXAMPLE
Sketch the graph of the following function
.
SOLUTION
We graph the function f (x) 1 x only for
those values of x that are less than or equal to
3.
Notice that for all values of x greater than 3,
there is no line.
9
Piece-Wise Functions
CONTINUED
Now we graph the function f (x) 4 only for
those values of x that are greater than 3.
Notice that for all values of x less than or
equal to 3, there is no line.
10
Piece-Wise Functions
CONTINUED
Now we graph both functions on the same set of
axes.
11
Quadratic Functions
12
Polynomial Functions
13
Rational Functions
14
Power Functions
15
Absolute Value Function