Download PC Sec. 1.2-1.4 Study Guide Haggenmaker Fall 2013

PC Sec. 1.2-1.4 Study Guide
Haggenmaker
Fall 2013-2014
Short Answer
1. A lake’s fish population over eight years is modeled by p(x) = 1.96x3 – 30x2 + 196x + 244. Use the function to
estimate p(2) and p(6), the populations in the second and sixth years.
2. Find f (a + 1) for f (x) = 2(x – 1)2 + 3x.
3. What is the domain and range of the function shown in the graph?
4. Find the average rate of change of f (x) = 2.5x2 – 7x + 5 on the interval [2, 5].
5. Evaluate f (–2) if f (x) = 3x2 – 2x.
6. Use the graph of f to find the domain and range of the function.
7. Graph f(x) = x3 – 4x using a graphing calculator. Determine whether the function is even, odd, or neither. If
even or odd, describe the symmetry of the graph.
Determine whether the function is continuous or discontinuous at the given x-value.
8.
9.
10. Use the graph of f (x) to describe its end behavior.
11. Find the average rate of change of f (x) on the interval [–3, –1].
Use the graph to determine the domain and range of the relation.
y
12.
x
y
13.
x
14.
y
1
–4
4
x
–1
15. Find
for
.
16. Use the graph of f(x) to estimate f(3).
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
–4
–6
–8
–10
2
4
6
8
10
x
17. Identify the y-intercept and zeros of
.
18. Use the graph below to identify the domain and range.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
19. Given the point
determine the points that are symmetric to this point with respect to the x-axis, the
y-axis, and the origin respectively.
20. The graph below is a portion of a complete graph. Sketch the complete graph assuming it is symmetric with
respect to the x-axis.
y
10
–10
10
x
–10
21. Is the following function an even function, an odd function, or neither?
22. Determine between which consecutive integers the real zeros of
[-10, 10].
are located on the interval
23. Determine between which consecutive integers the real zeros of
interval [-10, 10].
are located on the
Without graphing, describe the end behavior of the graph of the function.
24.
25.
26.
Graph the function. Determine the interval(s) for which the function is increasing and the interval(s) for
which the function is decreasing.
27.
28.
29. Find the relative minimum and the relative maximum points for the graph of
30. Estimate to the nearest 0.5 unit and classify the extrema for the graph of f(x).
y
32
28
24
20
16
12
8
4
–5
–4
–3
–2
–1
–4
–8
–12
–16
–20
–24
–28
–32
1
2
3
4
5
x
31. Estimate to the nearest 0.5 unit and classify the extrema for the graph of f(x).
y
70
60
50
40
30
20
10
–5
–4
–3
–2
–1
–10
1
2
3
4
5
x
–20
–30
–40
–50
–60
–70
32. Find the average rate of change of
on [5, 10]. Round your answer to the nearest hundredth.
Estimate and classify the critical points for the graph of each function.
33.
y
2
1
–2
–1
1
–1
–2
2
x
PC Sec. 1.2-1.4 Study Guide
Answer Section
Haggenmaker
SHORT ANSWER
1. ANS:
532; 763
2. ANS:
2a2 + 3a + 3
3. ANS:
;
4. ANS:
10.5
5. ANS:
16
6. ANS:
7. ANS:
odd; symmetric about origin
8. ANS:
discontinuous; jump
9. ANS:
discontinuous; infinite
10. ANS:
11. ANS:
–43
12. ANS:
Domain:
;
Range:
;
No, it fails the vertical line test.
OBJ: 1-1.2 Identify and evaluate functions and state their domains.
NAT: 2
TOP: Functions
13. ANS:
Domain: all positive real numbers, including zero;
Range: all real numbers;
No, it fails the vertical line test.
OBJ: 1-1.2 Identify and evaluate functions and state their domains.
NAT: 2
TOP: Functions
14. ANS:
Domain: all real numbers;
Range:
;
Yes, for any value of x there is only one value of y.
OBJ: 1-1.2 Identify and evaluate functions and state their domains.
Fall 2013-2014
NAT: 2
15. ANS:
TOP: Functions
=
OBJ: 1-1.2 Identify and evaluate functions and state their domains.
NAT: 2
TOP: Functions
16. ANS:
f(3) = 3
OBJ: 1-2.1 Use graphs of functions to estimate function values and find domains, ranges, y-intercepts, and
zeros of functions. NAT: 2
STA: 9-12.P.4
TOP: Analyzing Graphs of Functions and Relations
17. ANS:
y-intercept: –12
zeros: 1, –1
OBJ: 1-2.1 Use graphs of functions to estimate function values and find domains, ranges, y-intercepts, and
zeros of functions. NAT: 2
STA: 9-12.P.4
TOP: Analyzing Graphs of Functions and Relations
18. ANS:
D: [-6, 6), [7, )
R: [-3, )
OBJ: 1-2.1 Use graphs of functions to estimate function values and find domains, ranges, y-intercepts, and
zeros of functions. NAT: 2
STA: 9-12.P.4
TOP: Analyzing Graphs of Functions and Relations
19. ANS:
OBJ: 1-2.2 Explore symmetries of graphs, and identify even and odd functions.
NAT: 2
STA: 9-12.P.4
TOP: Analyzing Graphs of Functions and Relations
20. ANS:
y
10
–10
10
x
–10
OBJ: 1-2.2 Explore symmetries of graphs, and identify even and odd functions.
NAT: 2
STA: 9-12.P.4
TOP: Analyzing Graphs of Functions and Relations
21. ANS:
odd function
OBJ: 1-2.2 Explore symmetries of graphs, and identify even and odd functions.
NAT: 2
STA: 9-12.P.4
TOP: Analyzing Graphs of Functions and Relations
22. ANS:
-1; 1;
OBJ: 1-3.1 Use limits to determine the continuity of a function, and apply the Intermediate Value Theorem
to continuous functions.
NAT: 2
STA: 9-12.P.10
TOP: Continuity, End Behavior, and Limits
23. ANS:
OBJ: 1-3.1 Use limits to determine the continuity of a function, and apply the Intermediate Value Theorem
to continuous functions.
NAT: 2
STA: 9-12.P.10
TOP: Continuity, End Behavior, and Limits
24. ANS:
As x g(x) 
As x g(x) 
OBJ: 1-3.2 Use limits to describe end behavior in functions.
NAT: 2
STA: 9-12.P.4 | 9-12.P.10
TOP: Continuity, End Behavior, and Limits
25. ANS:
As x f (x) 
As x f (x) 
OBJ: 1-3.2 Use limits to describe end behavior in functions.
NAT: 2
STA: 9-12.P.4 | 9-12.P.10
TOP: Continuity, End Behavior, and Limits
26. ANS:
As x h(x) 
As x h(x) 
OBJ: 1-3.2 Use limits to describe end behavior in functions.
NAT: 2
STA: 9-12.P.4 | 9-12.P.10
TOP: Continuity, End Behavior, and Limits
27. ANS:
y
30
20
10
–30
–20
–10
10
20
30
x
–10
–20
–30
increasing for
and
; decreasing for
and
OBJ: 1-4.1 Determine intervals on which functions are increasing, constant, or decreasing, and determine
maxima and minima of functions.
NAT: 2
STA: 9-12.P.4
TOP: Determine whether a function is increasing or decreasing on an interval.
28. ANS:
y
10
–10
10
x
–10
increasing for
decreasing for
OBJ: 1-4.1 Determine intervals on which functions are increasing, constant, or decreasing, and determine
maxima and minima of functions.
NAT: 2
STA: 9-12.P.4
TOP: Determine whether a function is increasing or decreasing on an interval.
29. ANS:
is a relative maximum;
is a relative minimum
OBJ: 1-4.1 Determine intervals on which functions are increasing, constant, or decreasing, and determine
maxima and minima of functions.
NAT: 2
STA: 9-12.P.4
TOP: Extrema and Average Rates of Change
30. ANS:
OBJ: 1-4.1 Determine intervals on which functions are increasing, constant, or decreasing, and determine
maxima and minima of functions.
NAT: 2
STA: 9-12.P.4
TOP: Extrema and Average Rates of Change
31. ANS:
OBJ: 1-4.1 Determine intervals on which functions are increasing, constant, or decreasing, and determine
maxima and minima of functions.
NAT: 2
STA: 9-12.P.4
TOP: Extrema and Average Rates of Change
32. ANS:
0.08
OBJ: 1-4.2 Determine the average rate of change of a function. NAT: 2
STA: 9-12.P.4
TOP: Extrema and Average Rates of Change
33. ANS:
(-0.6, 0.6), maximum; (0.4, -0.2), minimum; (1, 0), maximum; no points of inflection that are critical points
OBJ: 1-4.3 Visually locate critical points on the graphs of polynomial functions and determine if each
critical point is a minimum, a maximum, or point of inflection.
TOP: Extrema and Average Rates of Change