a gym offers three levels of membership based on the number of visits per month, as represented by the…

a gym offers three levels of membership based on the number of visits per month, as represented by the table. membership plans\n| max visits per month | cost per visit ($) | monthly fee ($) |\n| ---- | ---- | ---- |\n| 12 | 5 | 15 |\n| 16 | 4 | 32 |\n| 24 | 3 | 42 |\nkaleigh wants to know how much she will pay for her gym membership. which graph represents the total monthly cost at the gym as a function of the number of visits kaleigh plans to make each month?

a gym offers three levels of membership based on the number of visits per month, as represented by the table. membership plans\n| max visits per month | cost per visit ($) | monthly fee ($) |\n| ---- | ---- | ---- |\n| 12 | 5 | 15 |\n| 16 | 4 | 32 |\n| 24 | 3 | 42 |\nkaleigh wants to know how much she will pay for her gym membership. which graph represents the total monthly cost at the gym as a function of the number of visits kaleigh plans to make each month?

Answer

Explanation:

Step1: Define cost - function for each plan

For the first plan (max 12 visits): Let $x$ be the number of visits. The cost function $C_1(x)=5x + 15$ for $0\leq x\leq12$.

Step2: Define cost - function for the second plan

For the second plan (max 16 visits): The cost function $C_2(x)=4x + 32$ for $12\lt x\leq16$.

Step3: Define cost - function for the third plan

For the third plan (max 24 visits): The cost function $C_3(x)=3x + 42$ for $16\lt x\leq24$.

Step4: Analyze the behavior of the functions

The first function $C_1(x)$ is a linear function with a slope of 5 and y - intercept of 15. The second function $C_2(x)$ is a linear function with a slope of 4 and y - intercept of 32. The third function $C_3(x)$ is a linear function with a slope of 3 and y - intercept of 42. Each function is defined on a different interval of $x$ (number of visits).

Since the question only asks for the general approach to finding the graph and not to actually draw the graph, we have shown how to calculate the total monthly cost for different numbers of visits.

Answer:

The total monthly cost $C(x)$ is given by: [C(x)=\begin{cases}5x + 15, &0\leq x\leq12\4x + 32, &12\lt x\leq16\3x + 42, &16\lt x\leq24\end{cases}] The graph will be composed of three line - segments corresponding to these three linear functions on their respective intervals.