Question

1. Which of the following represents a function?

Answer 1

1. 3rd one, because for each x there's only one y.

2. The domain are x's, so it's {2, 4, 6, 8}

3. The range are y's, so it's {1, 2, 3, 4}

4.
$p=kd\\ 7=3k\\ k=\dfrac{7}{3}\\ p=\dfrac{7}{3}d\\ d=\dfrac{3}{7}p\\ d=\dfrac{3}{7}\cdot28=12$

5. $T(-4)=7-(-4)=7+4=11$

6. $f(x) = - |x| + 2$

7.
$C=kt\\ 800=4k\\ k=200\\ C=200t$

Answer 2

$1.\\\#1\ not\ because\ for\ x=-2\to y=2\ and\ y=6\\\#2\ not\ because\ for\ x=1\to y=1\ and\ y=2\\\#3\ \boxed{IT'S\ OK}\leftarrow answer\\\#4\ not\ because\ for\ x=1\to y=2\ and\ y=3\ and...$

$2.\ (x;\ y)\to x\in D-domain\\\\therefore:\\\\\{(2;1);\ (4;2);\ (6;\ 3);\ (8;\ 4)\}\\\\\boxed{The\ domain\ D=\{2;\ 4;\ 6;\ 8\}}$

$3.\ (x;\ y)\to y\in Range\\\\\{(2;\ 1);\ (4;\ 2);\ (6;\ 3);\ (8;\ 4)\}\\\\\boxed{the\ range:\{1;\ 2;\ 3;\ 4\}}$

$4.\\\frac{p}{d}=constans\\\\\frac{28}{d}=\frac{7}{3}\ \ \ \ |cross\ multiply\\\\7\cdot d=3\cdot28\ \ \ \ |divide\ both\ sides\ by\ 7\\\\d=\frac{84}{7}\\\\\boxed{d=12}$

$5.\ T(z)=7-z\\\\T(-4)\to z=-4\\\\put\ the\ value\ of\ z\ to\ (7-z):\\\\T(-4)=7-(-4)=7+4=\boxed{11}$

$6.\\y=|x|\to\ the\ axis\ of\ symmetry\ is\ OY\ (S_{OY})\\\\y=-|x|\to\ the\ axis\ of\ symmetry\ is\ OX\ (S_{OX})\\\\so....\ the\ y-intercept\ is\ (0;\ 2),\ therefore\ answer\ is\ \boxed{f(x)=-|x|+2}$

$7.\\\begin{array}{ccc}C&-&t\\800&-&4\end{array}\ \ \ \ |cross\ multiply\\\\4C=800t\ \ \ \ \ |divide\ both\ sides\ by\ 4\\\\\boxed{C=200t}$