Transcript Ch 2-6 Special Functions(2)

Special Functions
• Constant Function
ex. y = 4.95
The Charlie’s Smorgasbord Function
• Absolute Value Function
ex. y = | x |
absolute
Value
• Step (Greatest Integer) Function
ex. y = [ x ]
The Bob Barker “Price is Right” Function
• Piece-wise Function
ex. Made up of pieces!
Example 1 Step Function
Example 2 Constant Function
Example 3 Absolute Value Functions
Example 4 Piecewise Function
Example 5 Identify Functions
Psychology One psychologist charges for
counseling sessions at the rate of $85 per hour or
any fraction thereof. Draw a graph that represents
this solution.
Explore
The total charge must be a multiple of $85,
so the graph will be the graph of a step
function.
Plan
If the session is greater than 0 hours, but
less than or equal to 1 hour, the cost is
$85. If the time is greater than 1 hour, but
less than or equal to 2 hours, then the cost
is $170, and so on.
Solve
Use the pattern of times and costs to make a
table, where x is the number of hours of the
session and C(x) is the total cost. Then draw
the graph.
x
C(x)
85
170
255
340
425
Answer:
Examine Since the psychologist rounds any fraction of
an hour up to the next whole number, each
segment on the graph has a circle at the left
endpoint and a dot at the right endpoint.
Sales The Daily Grind charges $1.25 per pound of
meat or any fraction thereof. Draw a graph that
represents this situation.
Answer:
Graph
For every value of
horizontal line.
g(x) = –3
x
g(x)
–2
–3
0
1
0.5
–3
–3
–3
The graph is a
Answer:
Graph
Answer:
Graph
and
on the same
coordinate plane. Determine the similarities and
differences in the two graphs.
Find several ordered pairs for each function.
x
|x–3|
x
|x+2|
0
3
–4
2
1
2
–3
1
2
1
–2
0
3
0
–1
1
4
1
0
2
5
2
1
3
Graph the points and connect them.
Answer:
• The domain of both graphs
is all real numbers.
• The range of both graphs
is
• The graphs have the
same shape, but different
x-intercepts.
• The graph of g(x) is the
graph of f(x) translated
left 5 units.
Graph
and
on the same
coordinate plane. Determine the similarities and
differences in the two graphs.
Answer:
• The domain of both graphs
is all real numbers.
• The range of
is
The range of
is
• The graphs have the same
shape, but different y-intercepts.
• The graph of g(x) is the graph of f(x)
translated up 5 units.
Graph
and range.
Identify the domain
Step 1 Graph the linear function
for
Since 3 satisfies this
inequality, begin with a
closed circle at (3, 2).
Graph
and range.
Identify the domain
Step 2 Graph the constant
function
Since x does
not satisfy this
inequality, begin with an
open circle at (3, –1)
and draw a horizontal
ray to the right.
Graph
and range.
Identify the domain
Answer: The function is defined
for all values of x, so the domain
is all real numbers. The values
that are y-coordinates of points
on the graph are all real numbers
less than or equal to –2, so the
range is
Graph
and range.
Answer: The domain is all real
numbers. The range
is
Identify the domain
Determine whether the graph
represents a step function,
a constant function, an
absolute value function,
or a piecewise function.
Answer: Since this graph
consists of different
rays and segments,
it is a piecewise
function.
Determine whether the graph
represents a step function,
a constant function, an
absolute value function,
or a piecewise function.
Answer: Since this graph is
V-shaped, it is an
absolute value
function.
Determine whether each graph represents a step
function, a constant function, an absolute value
function, or a piecewise function.
a.
b.
Answer: constant
function
Answer: absolute value
function