¶ … relationship pass the vertical line test, for being a function?
What is its range?
What is its domain?
What are its X-intercepts, if any?
(3,0) (6,0)
What is its Y-intercept, if any?
What is the nature of the relationship (linear, quadratic, etc.)?
nonlinear and nonquadratic
What is the value of f (x) at x=-2? (3)
Does the relationship pass the vertical line test, for being a function?
What is its approximate range?
What is its approximate domain?
What are its X-intercepts, if any?
What are its Y-intercepts, if any?
What is the nature of the relationship (linear, quadratic, etc.)?
Elliptic
What is/are the approximate y-value(s) of the relationship at x=3? (2)
What is its range?
(-6, +?)
What is its domain?
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.
X-intercepts (-3,0) (2,0)
(x+3)(x-2) = 0
X = -3 or 2
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.
(0,-6)
Y = 0 + 0 -- 6
Y=-6 ( Value of y-intercept
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.)
(2,0)(1,0)(-1,0)
(x-2)(x-1)(x+1) = 0
X = 2, 1, or -1
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.
Y-intercept = (0,2)
Y = 0 -- 0 -- 0 + 2
Y= 2
Find the equation of the inverses of the following functions.
23.
Y =
24.
Y =
If
and:
25. Find
(3x+1) + (x+2) = 4x+3
26. Calculate
. 4(1) + 3 = 7
27. Find
(3x+1) -- (x+2) = 2x-1
28. Calculate
2(5)-1 = 10-1=9
29. Find
(3x+1)(x+2) = 3x2+6x+x+2 = 3x2+7x+2
30. Calculate
3(4) + 7(2) + 2 = 12 +14 +2 = 28
31. Find
32. Calculate
3(1)+1/(1)+2 = (4/3)
References:
Stewart, J., Redlin, L., & Watson, S. (2009). College algebra. Belmont, CA: Brooks/Cole, Cengage Learning
Blitzer, R. (2010). College algebra. Upper Saddle River, NJ: Pearson/Prentice Hall.
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