At home or in your community , look for the at least 3 situation that could represent function form the identified situation, write a sample problem and its corresponding function equation
Sure, here are three situations representing functions:
Situation 1: Baking Cookies
Sample Problem: You want to determine how long it takes to bake a batch of cookies depending on the number of cookies in the batch and the oven temperature.
Function Equation: T(c, t) = c * t
Explanation: T represents the time it takes to bake the cookies. The function depends on two variables: c, the number of cookies, and t, the oven temperature.
Situation 2: Going for a Run
Sample Problem: You want to calculate the number of calories burned while running, based on the distance covered and the runner's weight.
Function Equation: C(d, w) = d * w
Explanation: C represents the calories burned, which is a function of two variables: d, the distance covered in miles, and w, the runner's weight in pounds.
Situation 3: Watering Plants
Sample Problem: You need to determine how much water is required to keep a set of plants healthy based on the number of days since the last watering and the average temperature.
Function Equation: W(d, t) = (d + t) / 2
Explanation: W represents the amount of water needed, which is a function of two variables: d, the number of days since the last watering, and t, the average temperature.
To find situations that can be represented by a function form, and to create sample problems and their corresponding function equations, follow these steps:
1. Identify Variables: Determine the main variables involved in the situation or scenario. Variables are quantities that can vary or change.
2. Define the Function: Determine how the variables are related to each other. Does changing one variable affect another?
3. Create Sample Problems: Generate different scenarios or situations that can be described using the function. These problems should involve the identified variables and reflect real-world situations.
4. Write Function Equations: Once you have determined the relationship between variables, you can write the corresponding function equations. These equations will represent the mathematical relationship between the variables in the problem.
Here are three situations, sample problems, and their corresponding function equations:
Situation 1: Distance traveled by a car based on time.
Sample Problem: A car is traveling at a constant speed of 60 miles per hour. How far will it travel in 3 hours?
Function Equation: distance = speed * time, or d = 60t, where d is the distance traveled (in miles), t is the time (in hours), and 60 is the constant speed of the car (in miles per hour).
Situation 2: Cost of printing pages at a copy shop.
Sample Problem: A copy shop charges $0.10 per page for black and white prints. How much will it cost to print 20 black and white pages?
Function Equation: cost = price per page * number of pages, or c = 0.10p, where c is the cost (in dollars), p is the number of pages, and 0.10 is the price per page (in dollars).
Situation 3: Height of a thrown ball based on time.
Sample Problem: A ball is thrown into the air with an initial velocity of 25 meters per second. How high will it be after 2 seconds?
Function Equation: height = initial velocity * time - 0.5 * acceleration * time^2, or h = 25t - 0.5a(t^2), where h is the height (in meters), t is the time (in seconds), 25 is the initial velocity (in meters per second), and a is the acceleration (in meters per second squared).
Remember, these function equations represent the relationship between the variables in each situation. The variables should be meaningful and clearly defined based on the context of the problem you are trying to solve.