Relationship Pass The Vertical Line Test, For Essay

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¶ … 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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