Alg1 2.2.3

Bellringer A farmer wants to convert three different-sized greenhouses to solar power. He needs 1,500 square feet of solar panels for his small greenhouse, 2,100 square feet of panels for his medium greenhouse, and 2,800 square feet of panels for his large greenhouse. The farmer gets bids from three different companies, each with different pricing. The bids are as follows, where x is the number of square feet of panels needed for each greenhouse, and y is the cost: Company A charges $2,000 for installation per greenhouse, and an additional $2.00 per square foot of panels. The function for this situation is y(A) = 2000 + 2(x). Company B charges $3,000 for installation per greenhouse, and an additional $1.50 per square foot of panels. The function for this situation is y(B) = 3000 + 1.5(x). Company C charges $4,200 for installation per greenhouse, and an additional $1.00 per square foot of panels. The function for this situation is y(C) = 4200 + x. 1. Which company will charge the least for the small greenhouse? 2. Which company will charge the least for the medium greenhouse? 3. Which company will charge the least for the large greenhouse? 4. If the farmer decides to hire a single company to convert all three greenhouses, which company will be the least expensive?

Bellringer-debrief

Bellringer-debrief

Bellringer-debrief

Bellringer-debrief

Standard F–IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Learning Target I can identify mathematical relationships and express them using function notation. I can define a reasonable domain, which depends on the context and/or mathematical situation for a function, focusing on linear functions. I can evaluate functions at a given input in the domain, focusing on linear functions. I can interpret statements that use functions in terms of real world situations, focusing on linear functions.

Mini Lesson Functions can be evaluated for values of variables. To evaluate a function such as f(x), substitute values in the domain for all occurrences of x. To evaluate f(2) in f(x) = x + 4, replace x with 2 and simplify: f(2) = (2) + 4 = 6. This means that f(2) = 6. The coordinates of a point on the graph of a function can be written as an ordered pair: (x, (f(x)).

Work Session Example 1 Evaluate f(x) = 4x – 7 over the domain of f , {1, 2, 3, 4}. What is the range of f ?

Work Session Example 2 Evaluate g(x) = 3x + 1 over the domain of g, {0, 1, 2, 3}. What is the range of g?

Work Session Example 3 Raven started an online petition calling for more vegan options in the school cafeteria. So far, the number of signatures has doubled every day. She started with 32 signatures on the first day. Raven’s petition can be modeled by the exponential function f(x) = 32(2)x. Evaluate f(3) and interpret the results in terms of the petition.

Closing

Homework Practice 2.2.3: Function Notation and Evaluating Functions #1-10 ODD