Math Case Homework
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See the figure on the right. This is a portion of a plot that continues indefinitely in both directions. E1. Does the relationship pass the vertical line test, for being a function? Yes. Any vertical line through the X-axis will intercept the plot at exactly one point. E2. What is its range? (-, +) E3. What is its domain? (-, +) E4. What are its X-intercepts, if any? (4,0) E5. What is its Y-intercept, if any? (0,-2) E6. What is the nature of the relationship (linear, quadratic, etc.)? Linear. E7. What is the value of f(x) at x=2? -1 |
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Problems:
See the figure below. The heavy line represents one function that continues indefinitely in the directions indicated by the arrows.
1. Does the relationship pass the vertical line test, for being a function?
2. What is its range?
3. What is its domain?
4. What are its X-intercepts, if any?
5. What is its Y-intercept, if any?
6. What is the nature of the relationship (linear, quadratic, etc.)?
7. What is the value of f(x) at x=-2?
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The figure below represents a relationship in the X-Y plane.
8. Does the relationship pass the vertical line test, for being a function?
9. What is its approximate range?
10. What is its approximate domain?
11. What are its X-intercepts, if any?
12. What are its Y-intercepts, if any?
13. What is the nature of the relationship (linear, quadratic, etc.)?
14. What is/are the approximate y-value(s) of the relationship at x=3?
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The figure below is a partial plot of the equation . It is a function.
15. What is its range?
16. What is its domain?
17. Determine the approximate x-intercepts by inspection; that is, looking at the plot. Verify these results by calculating the x-intercepts (roots of the equation). Show your calculations in detail.
18. Determine the approximate y-intercept(s) by inspection. Verify these results by calculating the value of the y-intercept(s). Show your calculations in detail.
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The figure below is a partial plot of the equation . It is a function.
19. What is its range?
20. What is its domain?
21. Determine the approximate x-intercepts by inspection; that is, looking at the plot. Verify these results by calculating the x-intercepts (roots of the equation). Show your calculations in detail. (Hint: Find the factors using polynomial division.)
22. Determine the approximate y-intercept(s) by inspection. Verify these results by calculating the value of the y-intercept(s). Show your calculations in detail.
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Find the equation of the inverses of the following functions.
— end —
3
f(x)x5
=+
6
f(x)7
x
=+
f(x)3×1
=+
g(x)x2
=+
(fg)(x)
+
(fg)(1)
+
(fg)(x)
–
(fg)(5)
–
(fg)(x)
(fg)(2)
f
(x)
g
æö
ç÷
èø
f
(1)
g
æö
ç÷
èø
12
34
5678
9
1
2
3
4
5
-4
-3
-2
-1
-5-4-3-2-1
0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
-4
-3
-2
-1
-5
-4
-3
-2
-1
0
12
34
5678
9
1
2
3
4
5
-1
-2-1
0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
-1
-2
-1
