Introduction to Functions

1. function
2. function
3. function
4. function
5. function
6. function
7. function
8. function
9. not a function
10. [latex]f(-3)=-11[/latex];
    [latex]f(2)=-1[/latex];
    [latex]f(-a)=-2a-5[/latex];
    [latex]-f(a)=-2a+5[/latex];
    [latex]f(a+h)=2a+2h-5[/latex]
11. [latex]f(-3)=\sqrt{5}+5[/latex];
    [latex]f(2)=5[/latex];
    [latex]f(-a)=\sqrt{2+a}+5[/latex];
    [latex]-f(a)=-\sqrt{2-a}-5[/latex];
    [latex]f(a+h)=\sqrt{2-a-h}+5[/latex]
12. [latex]f(-3)=2[/latex];
    [latex]f(2)=1-3=-2[/latex];
    [latex]f(-a)=|-a-1|-|-a+1|[/latex];
    [latex]-f(a)=-|a-1|+|a+1|[/latex];
    [latex]f(a+h)=|a+h-1|-|a+h+1|[/latex]
13. [latex]\dfrac{g(x)-g(a)}{x-a}=x+a+2[/latex], [latex]x\neq a[/latex]
14. 1. [latex]f(-2)=14[/latex]
    2. [latex]x=3[/latex]
15. 1. [latex]f(5)=10[/latex]
    2. [latex]x=-1[/latex] or [latex]x=4[/latex]
16. 1. [latex]f(t)=6-\dfrac{2}{3}t[/latex]
    2. [latex]f(-3)=8[/latex]
    3. [latex]t=6[/latex]
17. not a function
18. function
19. function
20. function
21. function
22. function
23. 1. [latex]f(0)=1[/latex]
    2. [latex]f(x)=-3[/latex], [latex]x=-2[/latex] or [latex]x=2[/latex]
24. not a function so it is also not a one-to-one function
25. one-to-one function
26. function, but not one-to-one
27. function
28. function
29. not a function
30. [latex]f(x)=1[/latex], [latex]x=2[/latex]
31. 1. [latex]g(5000)=50[/latex]
    2. The number of cubic yards of dirt required for a garden of [latex]100[/latex] square feet is [latex]1[/latex].
32. 1. The height of a rocket above ground after [latex]1[/latex] second is [latex]200[/latex] ft.
    2. The height of a rocket above ground after [latex]2[/latex] seconds is [latex]350[/latex] ft.

Domain and Range

1. [latex](-\infty,\infty)[/latex]
2. [latex](-\infty,3][/latex]
3. [latex](-\infty,\infty)[/latex]
4. [latex](-\infty,\infty)[/latex]
5. [latex](-\infty,-\dfrac{1}{2})\cup(-\dfrac{1}{2},\infty)[/latex]
6. [latex](-\infty,-11)\cup(-11,2)\cup(2,\infty)[/latex]
7. [latex](-\infty,-3)\cup(-3,5)\cup(5,\infty)[/latex]
8. [latex](-\infty,5)[/latex]
9. [latex][6,\infty)[/latex]
10. [latex](-\infty,-9)\cup(-9,9)\cup(9,\infty)[/latex]
11. domain: [latex][2,8][/latex], range: [latex][6,8][/latex]
12. domain: [latex][-4,4][/latex], range: [latex][0,2][/latex]
13. domain: [latex][-5,3)[/latex], range: [latex][0,2][/latex]
14. domain: [latex](-\infty,1][/latex], range: [latex][0,\infty)[/latex]
15. domain: [latex][-6,-\dfrac{1}{6}]\cup[\dfrac{1}{6},6][/latex]; range: [latex][-6,-\dfrac{1}{6}]\cup[\dfrac{1}{6},6][/latex]
16. domain: [latex][-3,\infty)[/latex]; range: [latex][0,\infty)[/latex]
17. domain: [latex](-\infty,\infty)[/latex]
    
18. domain: [latex](-\infty,\infty)[/latex]
    
19. domain: [latex](-\infty,\infty)[/latex]
    
20. domain: [latex](-\infty,\infty)[/latex]
    
21. [latex]f(-3)=1[/latex]; [latex]f(-2)=0[/latex]; [latex]f(-1)=0[/latex]; [latex]f(0)=0[/latex]
22. [latex]f(-1)=-4[/latex]; [latex]f(0)=6[/latex]; [latex]f(2)=20[/latex]; [latex]f(4)=34[/latex]
23. [latex]f(-1)=-5[/latex]; [latex]f(0)=3[/latex]; [latex]f(2)=3[/latex]; [latex]f(4)=16[/latex]
24. domain: [latex](-\infty,1)\cup(1,\infty)[/latex]

Rates of Change and Behavior of Graphs

1. [latex]4x+2h[/latex]
2. [latex]\dfrac{-1}{13(13+h)}[/latex]
3. [latex]3h^2+9h+9[/latex]
4. [latex]4x+2h-3[/latex]
5. [latex]\dfrac{4}{3}[/latex]
6. increasing on [latex](-\infty,-2.5)\cup(1,\infty)[/latex], decreasing on [latex](-2.5,1)[/latex]
7. increasing on [latex](-\infty,1)\cup(3,4)[/latex], decreasing on [latex](1,3)\cup(4,\infty)[/latex]
8. [latex]-4[/latex]
9. [latex]27[/latex]
10. [latex]-0.167[/latex]
11. [latex]2.7[/latex] gallons per minute
12. approximately [latex]-0.6[/latex] milligrams per day