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.\nmembership 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.\nmembership 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: Analyze the second plan (max 16 visits)

The cost function $C_2(x)=4x + 32$ for $12\lt x\leq16$.

Step3: Analyze the third plan (max 24 visits)

The cost function $C_3(x)=3x + 42$ for $16\lt x\leq24$.

Step4: Check the slopes and y - intercepts of the functions

The first function $C_1(x)$ has a slope of 5 and y - intercept of 15. The second function $C_2(x)$ has a slope of 4 and y - intercept of 32. The third function $C_3(x)$ has a slope of 3 and y - intercept of 42. As the number of visits increases, the slope of the cost - function decreases and the y - intercept increases.

Step5: Match with the graphs

The graph should have three linear segments with decreasing slopes and increasing y - intercepts at the break - points (12 and 16 visits).

Answer:

The graph that has three linear segments where the slope decreases and the y - intercept increases at the break - points of 12 and 16 visits. (Since no specific graph options are labeled, a general description of the correct graph is provided).