Question

1. the cost of large boxes of cruncho breakfast cereal at a save rite grocery store is represented by the function f, shown in the graph. at members save shopping club, the cost of a lifetime membership is $20, and each large box of cruncho breakfast cereal costs $3. the function g represents the cost of large boxes of cruncho breakfast cereal at members save.

a. which function has the greater value for x = 0? what does this value represent?
b. which function has the lesser value for x = 10? what does the answer mean in terms of buying cruncho cereal at the two stores?
c. which function has the lesser value for x = 25? what does the answer mean in terms of buying cruncho cereal at the two stores?

Explanation:

A.

Step1: Find \(f(0)\) and \(g(0)\)

• For \(f(x)\): Assume \(f(x)\) is linear (from graph points \((1,4)\), \((2,8)\), slope \(m = 4\), \(y=4x\), so \(f(0)=4\times0=0\).
• For \(g(x)=3x + 20\), \(g(0)=3\times0+20 = 20\).

Step2: Compare and interpret

• \(g(0)>f(0)\). \(g(0)\) is membership - fee (cost when \(x = 0\) boxes).

B.

Step1: Calculate \(f(10)\) and \(g(10)\)

• \(f(10)=4\times10=40\).
• \(g(10)=3\times10+20=50\).

Step2: Compare and interpret

• \(f(10)<g(10)\). Cheaper at Save Rite for 10 boxes.

C.

Step1: Calculate \(f(25)\) and \(g(25)\)

• \(f(25)=4\times25=100\).
• \(g(25)=3\times25+20=95\).

Step2: Compare and interpret

• \(g(25)<f(25)\). Cheaper at Members Save for 25 boxes.

Answer:

A.

• Function \(f\) has the greater value for \(x = 0\).
• Value for \(f(0)\): From the graph, when \(x = 0\) (no boxes bought), \(y=f(0)=4\). For \(g(x)=3x + 20\), when \(x = 0\), \(g(0)=3\times0+20=20\). Wait, no, reverse. Wait, no:
• For function \(f\) (from the graph, assume it's a linear function passing through \((1,4)\), \((2,8)\), \((3,12)\), \((4,16)\), so \(f(x)=4x\). Then \(f(0)=4\times0 = 0\). For \(g(x)=3x+20\), \(g(0)=20\). So \(g\) has a greater value at \(x = 0\). This value (\(g(0) = 20\)) represents the cost of a lifetime membership at Members Save (since when \(x=0\) (no cereal boxes bought), the cost is just the membership fee).

B.

• Function \(g\) has the lesser value for \(x = 10\).
• \(f(10)=4\times10=40\).
• \(g(10)=3\times10 + 20=30+20=50\). Wait, no:
• Wait, \(f(x)\): from the graph points \((1,4)\), slope \(m=\frac{8 - 4}{2-1}=4\), \(y - 4=4(x - 1)\), \(y=4x\). So \(f(10)=4\times10 = 40\). \(g(10)=3\times10+20=50\). So \(f\) has lesser value. This means that when buying 10 boxes of Cruncho cereal, it is cheaper to buy at Save Rite (since \(f(10)=40<g(10) = 50\)).

C.

• Function \(g\) has the lesser value for \(x = 25\).
• \(f(25)=4\times25=100\).
• \(g(25)=3\times25+20=75 + 20=95\). This means that when buying 25 boxes of Cruncho cereal, it is cheaper to buy at Members Save (since \(g(25)=95<f(25)=100\)).