Write the following relation as sets of ordered pairs and find if it is a function:

$\left\{\left(x,y\right):y>x+1, x=1, 2 \mathrm{and} y=2,4,6\right\}$

Write the following relation as sets of ordered pairs and find if it is a function:

$\left\{\left(x,y\right):x+y=3, x,y\in \left\{\mathrm{0,1},2,3\right\}\right\}$

If $f$ is a function defined from $R$ to $R$ as follows: $f\left(x\right)=x^2$

Find the range of the function.

If $g$ is a function defined from $R$ to $R$ as follows:  $g\left(x\right)=\sin x$

Find the range of the function.

If $h$ is a function defined from $R$ to $R$ as follows: $h\left(x\right)=x^2+1$

Find the range of the function.

Let $X=\{\mathrm{1,} 2, \mathrm{3,} 4\}$ and $Y=\{\mathrm{1,} 5, \mathrm{9,} \mathrm{11,} \mathrm{15,} 16\}$

Determine whether the following set is a function from $X$ to $Y$

$f_1=\left\{\left(\mathrm{1,1}\right), \left(2, 11\right), \left(3, 1\right), \left(4, 15\right)\right\}$

Let $X=\{\mathrm{1,2},\mathrm{3,4}\}$ and $Y=\{\mathrm{1,5},\mathrm{9,11,15,16}\}$

Determine whether the following set is a function from $X$ to $Y$:

$f_2=\left\{\left(\mathrm{1,1}\right),\left(\mathrm{2,7}\right),\left(\mathrm{3,5}\right)\right\}$

Let $X=\{\mathrm{1,2},\mathrm{3,4}\}$ and $Y=\{\mathrm{1,5},\mathrm{9,11,15,16}\}$

Determine whether the following set is a function from $X$ to $Y$:

$f_3=\left\{\left(\mathrm{1,5}\right),\left(2,9\right)\left(\mathrm{3,1}\right),\left(\mathrm{4,5}\right),\left(\mathrm{2,11}\right)\right\}$.