Question

CELL PHONES The cost of sending cell phone pictures is given by $y=0.25x$where $x$is the number of pictures that you send. Write the equation in function notation and then find $f\left(5\right)$and$f\left(12\right)$.What do these values represent? Determine the domain and range of this function.

Short answer

We can write the equation $y=0.25x$as $f\left(x\right)=0.25x,f\left(5\right)=1.25,f\left(12\right)=3$, the value $f\left(5\right)$represents the spending of $\$1.25$for sending 5 pictures and the value $f\left(12\right)$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 $y=\left\{0.25,0.50,0.75,1,1.25,\mathrm{...}\right\}$ .

Step-by-step solution

Step 1. Given.

The given equation is, $y=0.25x$.

Step 2. Calculation.

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

The functional representation of the equation $y=0.25x$is

$f\left(x\right)=0.25x$

Substituting $x=5$in the given function 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 $f\left(12\right)$

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

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 any positive real number. $y=\left\{0.25,0.50,0.75,1,1.25,\mathrm{...}\right\}$.

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 $y=\left\{0.25,0.50,0.75,1,1.25,\mathrm{...}\right\}$.

Step 3. Conclusion.

Thus, the domain and range of the function$y=0.25x$ is obtained.