Question

A husband and wife attend the local recreation center. The husband pays a flat rate of $125 for one year, shown as f(x). The wife pays $6 per visit, shown as g(x). Which function shows the correct combination of these two functions to represent the total cost to them of attending the recreation center in one year, shown as h(x)?
a.f(x)=125x,g(x)=6,h(x)=125x+6
b.f(x)=125,g(x)=6,h(x)=6+125
c.f(x)=125x,g(x)=6(x),h(x)=125x+6x
d.f(x)=125,g(x)=6x,h(x)=6x+125

Answer 1

Answer: $h(x)=125+6x$

Step-by-step explanation:

Given: The husband pays a flat rate of $125 for one year.

such that $f(x)=125$

Let x be the number of visits.

The wife pays $6 per visit.

$g(x)=6x$

Let h(x) be the combination of the above functions, that is

$h(x)=f(x)+g(x)\\\\\Rightarrow\ h(x)=125+6x$

Hence, function shows the correct combination of these two functions to represent the total cost to them of attending the recreation center in one year is $h(x)=125+6x$

Answer 2

Dissecting the information:

"The husband pays a flat rate of $125 for one year" means he pays $125 irrespective of how many times he visits (x). Doesn't depend on the number of visits (x).

"The wife pays $6 per visit" means that she pays $6x, of course, being dependent on the number of visits (x).

Hence, their total cost is sum of their individual costs, $(125+6x).

Husband's cost is f(x)=125, wife's cost is g(x)=6x, and total cost is h(x)=125+6x. Option D is correct answer.

ANSWER: D