Answer :
To solve this problem, we need to find the total cost of apples given the number of pounds. We are provided with the cost per pound and the function that represents this relationship.
1. Define the function rule:
The cost function [tex]\( f(x) \)[/tex] that gives the total cost of apples in terms of the number of pounds [tex]\( x \)[/tex] is:
[tex]\[ f(x) = 1.25x \][/tex]
This equation means that for every pound of apples, we multiply by their cost per pound, which is [tex]$1.25. 2. Evaluate the function for specific values of \( x \): - When \( x = 0 \): \[ f(0) = 1.25 \times 0 = 0 \] So, the cost of 0 pounds of apples is $[/tex]0.
- When [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 1.25 \times 1 = 1.25 \][/tex]
So, the cost of 1 pound of apples is [tex]$1.25. - When \( x = 2 \): \[ f(2) = 1.25 \times 2 = 2.50 \] So, the cost of 2 pounds of apples is $[/tex]2.50.
- When [tex]\( x = 6 \)[/tex]:
[tex]\[ f(6) = 1.25 \times 6 = 7.50 \][/tex]
So, the cost of 6 pounds of apples is [tex]$7.50. - When \( x = 10 \): \[ f(10) = 1.25 \times 10 = 12.50 \] So, the cost of 10 pounds of apples is $[/tex]12.50.
3. Summarize the results in a table:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of pounds } (x) & \text{Cost of apples } (f(x)) \\ \hline 0 & 0 \\ \hline 1 & 1.25 \\ \hline 2 & 2.50 \\ \hline 6 & 7.50 \\ \hline 10 & 12.50 \\ \hline x & 1.25x \\ \hline \end{array} \][/tex]
This table provides the cost of apples for different quantities (in pounds) based on the function [tex]\( f(x) = 1.25x \)[/tex].
1. Define the function rule:
The cost function [tex]\( f(x) \)[/tex] that gives the total cost of apples in terms of the number of pounds [tex]\( x \)[/tex] is:
[tex]\[ f(x) = 1.25x \][/tex]
This equation means that for every pound of apples, we multiply by their cost per pound, which is [tex]$1.25. 2. Evaluate the function for specific values of \( x \): - When \( x = 0 \): \[ f(0) = 1.25 \times 0 = 0 \] So, the cost of 0 pounds of apples is $[/tex]0.
- When [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 1.25 \times 1 = 1.25 \][/tex]
So, the cost of 1 pound of apples is [tex]$1.25. - When \( x = 2 \): \[ f(2) = 1.25 \times 2 = 2.50 \] So, the cost of 2 pounds of apples is $[/tex]2.50.
- When [tex]\( x = 6 \)[/tex]:
[tex]\[ f(6) = 1.25 \times 6 = 7.50 \][/tex]
So, the cost of 6 pounds of apples is [tex]$7.50. - When \( x = 10 \): \[ f(10) = 1.25 \times 10 = 12.50 \] So, the cost of 10 pounds of apples is $[/tex]12.50.
3. Summarize the results in a table:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of pounds } (x) & \text{Cost of apples } (f(x)) \\ \hline 0 & 0 \\ \hline 1 & 1.25 \\ \hline 2 & 2.50 \\ \hline 6 & 7.50 \\ \hline 10 & 12.50 \\ \hline x & 1.25x \\ \hline \end{array} \][/tex]
This table provides the cost of apples for different quantities (in pounds) based on the function [tex]\( f(x) = 1.25x \)[/tex].
