Question

problem 3
a restaurant sells three different salads.
they use the functions ( c(x) ), ( g(x) ), and ( p(x) ) to represent the cost of their caesar, garden, and pasta salads in dollars, with ( x ) additional ingredients added.
explain the meaning of each statement.
( g(0) = 10 )
( g(3) > c(1) )
( p(2) < g(3) )

Explanation:

1. For \( g(0) = 10 \): The function \( g(x) \) represents the cost of a garden salad (assuming \( g(x) \) is the cost function for garden salad) with \( x \) additional ingredients. When \( x = 0 \) (no additional ingredients), the cost of the garden salad is $10.
2. For \( g(3)>c(1) \): \( g(3) \) is the cost of a garden salad with 3 additional ingredients, and \( c(1) \) is the cost of a caesar salad (assuming \( c(x) \) is the cost function for caesar salad) with 1 additional ingredient. This statement means the cost of a garden salad with 3 additional ingredients is greater than the cost of a caesar salad with 1 additional ingredient.
3. For \( p(2)<g(3) \): \( p(2) \) is the cost of a pasta salad (assuming \( p(x) \) is the cost function for pasta salad) with 2 additional ingredients, and \( g(3) \) is the cost of a garden salad with 3 additional ingredients. This statement means the cost of a pasta salad with 2 additional ingredients is less than the cost of a garden salad with 3 additional ingredients.

Answer:

• \( g(0) = 10 \): Cost of garden salad with 0 additional ingredients is $10.
• \( g(3)>c(1) \): Cost of garden salad (3 add'l ingredients) > cost of caesar salad (1 add'l ingredient).
• \( p(2)<g(3) \): Cost of pasta salad (2 add'l ingredients) < cost of garden salad (3 add'l ingredients).