Expert: Robi Bhattacharjee - 10/11/2008

Question
Hello,
Can you please help with these? I would greatly appeciate it.

1) True or False - The following relation is a function: {(1, 2), (3, 4), (5, 5)}
                                False?

2) True or False - The following relation is a function: {(3, 4), (3, 5, (4, 4), (4, 5)}
                                True?

3) Evaluate f(x) = 3x + 7 at 5(4)
      I know it has to be either 45, 14, 19, or 28 and my guess is 14


4) f(x) = 4x^2 - 1 / c^2 at f(-2)
    I know it has to be either 4/15, 15/4, 1/2 or 11/20  my guess is 15/4


5) f(x) = x^3 - x
    I know it has to be either an odd function, an even function, or neither and my guess is that its an odd function.


6) f(x) = 2x^2 + x^4 + 1 Is either an odd function, an even function, or neither. My guess is that its an even function.

7) Write an equation in slope-interception form for the line passing through (3, 5) and (8, 15)

I think this one is a..

a) y = 2x - 1
b) y = 3x + 8
c) y = -2x - 1
d) y = x + 15


8) Write an equation in slope-intercept form for the line passing through points (-2, 0) and (0, 2)

I think this one is b..

a) y = -2x + 1
b) y = x + 4
c) y = x + 2
d) y = -x


9) Find the slope for the line passing through points (2, 1) and (3, 4)
    Has to be either 7, 6, 1 or 3 and I think its 6

10) Find the slope for the line passing through points (6, -4) and (4, 2)
      Has to be either 1, 0, 10 or -1 and I think its 10

Answer
Hello Andy,

I usually don't answer so many questions at a time, but I'll make an exception. Just know that usually I answer 1-3 questions.

So here are the solutions.

1)This is a function. All you have to do to check if something is a functions is to make sure each x value has only one y value. However bit is okay for two x values to have the same y value. note that all points in math are of form (x,y). So 1 - 2,  3 - 4,  5 - 5. each x value has only one y value so it IS a function. True

2)3 - 4,  3 - 5,  4 -4,  5-5, This is not a functions since 3 has two values namely 4 and 5 and 4 has two values namely 4 and 5.

3)I'm not sure what you meant on this question, but I think the question was evaluate f(x)= 3x + 7 at x=4. All you do is stick 4 in where x is. So it would be 3(4) + 7 = 12 + 7 = 19.

4)I'm not sure what you meant on this one either. Did you mean (4x^2 -1)/x^2 at f(-2). If so then it would be (4*4 - 1)/4 = 15/4.

5)For these types of problems, it is helpful to know that for odd functions -f(x) = f(-x) and for even functions f(x)= f(-x).
So f(x) = x^3 - x  f(-x) = -x^3 + x = -(x^3 - x) = -f(x). So it is an odd function.

6)f(x) = 2x^2 + x^4 + 1  f(-x) = 2x^2 + x^4 + 1 = f(x) so it is even.

7)(3,5) and (8,15). So the slope is rise/run = 10/5 = 2 so 2(x-3) = y - 5 so 2x - 1 = y. (a)

8)slope = rise/run = 1 so y - 2 = x so y = x + 2 (c)

9)rise/run = 3

10)rise/run = -3. This is the right answer. Check the question to make sure you copied in the correct choices.

I hope this helped,
Robi