Question

evaluate each function for the given value of x, and write the input and output as an ordered pair.

1. $f(x)=17x + 3$ for $x = 4$

$f(4)=17(4)+3$
$f(4)=71$

1. $g(x)=-\frac{2x + 1}{3}$ for $x=-5$

$g(-5)=-\frac{2(-5)+1}{3}$
$g(-5)=-\frac{-9}{3}$
$g(-5)=3$

1. $h(x)=\frac{7}{3}x - 9$ for $x = 3$

$h(3)=\frac{7}{3}(3)-9$
$h(3)=7 - 9$
$h(3)=-2$

1. $f(x)=\frac{2}{9x}-\frac{9}{2}$ for $x = 9$

$f(9)=\frac{2}{9(9)}-\frac{9}{2}$
write a function to represent the following and then evaluate for the given value.

1. a cell - phone plan cost $50 per month and then $15 per gigabyte of data. write a function to represent the total cost for a month based on the gigabytes of data used. evaluate your function for 8 gigabytes.

$x =$ gigabytes
$c(x)=15x + 50$
$c(8)=15(8)+50$
$c(8)=120 + 50$
$c(8)=170$

Explanation:

Step1: Evaluate $f(x)=17x + 3$ at $x = 4$

Substitute $x = 4$ into the function: $f(4)=17\times4+3=68 + 3=71$. The ordered - pair is $(4,71)$.

Step2: Evaluate $g(x)=-\frac{2x + 1}{3}$ at $x=-5$

Substitute $x=-5$ into the function: $g(-5)=-\frac{2\times(-5)+1}{3}=-\frac{-10 + 1}{3}=-\frac{-9}{3}=3$. The ordered - pair is $(-5,3)$.

Step3: Evaluate $h(x)=\frac{7}{3}x-9$ at $x = 3$

Substitute $x = 3$ into the function: $h(3)=\frac{7}{3}\times3-9=7 - 9=-2$. The ordered - pair is $(3,-2)$.

Step4: Evaluate $f(x)=\frac{2}{9x}-\frac{9}{2}$ at $x = 9$

Substitute $x = 9$ into the function: $f(9)=\frac{2}{9\times9}-\frac{9}{2}=\frac{2}{81}-\frac{9}{2}=\frac{4 - 729}{162}=-\frac{725}{162}$. The ordered - pair is $(9,-\frac{725}{162})$.

Step5: Write and evaluate cost function

The cost function for the cell - phone plan is $C(x)=15x + 50$, where $x$ is the number of gigabytes of data used. When $x = 8$, $C(8)=15\times8+50=120 + 50=170$.

Answer:

1. $(4,71)$
2. $(-5,3)$
3. $(3,-2)$
4. $(9,-\frac{725}{162})$
5. $C(x)=15x + 50$, $C(8)=170$