Chapter 1.7, Problem 10CYU

To determine

To write: The equation $y=0.25x$ in function notation then find $f\left(5\right)$ and $f\left(12\right)$ , write the representation of these values and find the domain and range of this function.

Answer to Problem 10CYU

Thefunctional notation of the equation $y=0.25x$ is $f\left(x\right)=0.25x$ , $f\left(5\right)=1.25$ , $f\left(12\right)=3$ , $f\left(5\right)$ value represents the spending of $\$1.25$ for sending 5 pictures and the $f\left(12\right)$ represents the spending of $\$3$ for sending 12 pictures and the domain is $x=\left\{1,2,3,\mathrm{4...}\right\}$ and the range is $y=\left\{0.25,0.50,0.75,1,1.25,\mathrm{...}\right\}$ .

Explanation of Solution

Given information:

The equation is $y=0.25x$ .

Calculation:

Let $y=f\left(x\right)$ .

The functional notation of the equation $y=0.25x$ is as follows.

  $f\left(x\right)=0.25x$

Substitute $x=5$ in the function $f\left(x\right)=0.25x$ to find $f\left(5\right)$ .

  $\begin{array}{c}f\left(5\right)=0.25\left(5\right)\\ =1.25\end{array}$

Substitute $x=12$ in the function $f\left(x\right)=0.25x$ to find $f\left(12\right)$ .

  $\begin{array}{c}f\left(12\right)=0.25\left(12\right)\\ =3\end{array}$

The $f\left(5\right)$ value represents the spending of $\$1.25$ for sending 5 pictures and the $f\left(12\right)$ represents the spending of $\$3$ for sending 12 pictures.

The value of $x$ represents the domain which can be any natural number as $x=\left\{1,2,3,\mathrm{4...}\right\}$ and $f\left(x\right)$ represents the range of the function which can be nay positive real number as $y=\left\{0.25,0.50,0.75,1,1.25,\mathrm{...}\right\}$ .

The domain is $\left\{5,12\right\}$ and the range is $\left(\$1.25,\$3\right)$ .

Therefore, the functional notation of the equation $y=0.25x$ is $f\left(x\right)=0.25x$ , $f\left(5\right)=1.25$ , $f\left(12\right)=3$ , $f\left(5\right)$ value represents the spending of $\$1.25$ for sending 5 pictures and the $f\left(12\right)$ represents the spending of $\$3$ for sending 12 pictures and the domain is $x=\left\{1,2,3,\mathrm{4...}\right\}$ and the range is $y=\left\{0.25,0.50,0.75,1,1.25,\mathrm{...}\right\}$ .