I'm really having trouble with these types of equations. please help.?

Question

1. the following relation is a function: {(1,2),(3,4),(5,5)}
true or false?
2. {(3,4),(3,5),(4,4),(4,5)} true or false?
3. f(x)=X^3-x is it a odd, even function, or neither?
4. f(x)=3x+7 at f(4)
5. write a equation in slope-intercept form for the line passing through points (3,5) and (8,15) ?
6. Find the slope for the linepassing through points (2,1) and ( 3,4). ?
7. write a equation in slope-intercept form for the line passing through points (-2,0) and (0,2) ?

Answer 1

1) true. It's 1-to-1.

2) false. It's 1-to-many.

3) even for all integers

4) f(4) = 3(4) + 7 = 12 + 7 = 19

5) y = mx + b
y = (15-5)x/(8-3) + b {(y2 - y1) / (x2 - x1) is the slope }
y = 10x/5 + b
y = 2x + b
5 = 2(3) + b { Substitute one of the two points you were given }
5 = 6 + b { And solve for b }
b = -1
y = 2x - 1

6) (4-1)/(3-2) = 3/1 = 3

7) y = mx + b
y = (2-0)x/(0-(-2)) + b {(y2 - y1) / (x2 - x1) is the slope }
y = 2x/2 + b
y = x + b
2 = 0 + b { Substitute one of the two points you were given }
b = 2 { And solve for b }
y = x + 2

Answer 2

1. true. there is no x value paired with more than 1 y value.

2. false. 3→4 and 3→5. 4→4 and 4→5. Imagine you worked 4 hours. Is your pay $40 or $50? A function provides just 1 answer.

3. odd. f(-x) = (-x)^3 - (-x) = -x^3 + x = -(x^3 - x) = -f(x). the quick was is to see that all the exponents are odd.

4. f(4) = 3(4) + 7 = 19

5. 5→15, increases by 10. 3→8, increases by 5. slope = 10/5 = 2. so y = 2x + b, and plug in one point to find b:

(15) = 2(8) + b
b = -1

so y = 2x - 1

6. change from 1 to 4 is 3, from 2 to 3 is 1, so slope = 3/1 = 3.

7. slope is 2/2 = 1, and (0,2) IS the y-intercept, so y = x + 2.

Answer 3

1. If you can find the slope and the Y intercept you can make it into a function. once you have the slope by using deltaY/deltaX use the formula Y= Mx+b m=slope b=y intercept.
2. same as one.
3. thats a positive function. just graph it in your calculator. if it goues up from left to right then its even, if it goes doen from left to right then its odd
4. F(4) = 3(4) + 7
= 19
5. ok this you use the point to point form for finding a slope. which will be delta Y over delta X

(15-5)/ (8-3) = 10/5 which is just 1/2

6. do the same thing for this (4-1)/(3-2) = 3/1 which is 3

7. (2-0)/(0-(-2)) = 2/2 which is just 1

hope that helps.