Chapter 2 Section 6. Psychology One psychologist charges for counseling sessions at the rate of $85...
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Transcript of Chapter 2 Section 6. Psychology One psychologist charges for counseling sessions at the rate of $85...
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.
425
340
255
170
85
C(x)x
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 The graph is a horizontal line.
g(x) = –3
x g(x)
–2 –3
0 –3
1 –3
0.5 –3
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 |
0 3
1 2
2 1
3 0
4 1
5 2
x | x + 2 |
–4 2
–3 1
–2 0
–1 1
0 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.
• The domain of both graphs is all real numbers.
• 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.
Answer:
• The range of is The range of
is
Step 1 Graph the linear function for
Since 3 satisfies this inequality, begin with a
closed circle at (3, 2).
Graph Identify the domain and range.
Step 2 Graph the constant function
Since x doesnot satisfy this inequality, begin with an open circle at
(3, –1) and draw a horizontal ray to the right.
Graph Identify the domain and range.
Graph Identify the domain and range.
Answer: The function is defined
for all values of x, so the domainis 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 therange is
Determine whether the graphrepresents a step function, a constant function, anabsolute value function, or a piecewise function.
Answer: Since this graphconsists of differentrays and segments, it is a piecewisefunction.
Determine whether the graphrepresents a step function, a constant function, anabsolute 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 valuefunction