Standard+2.1.c-lo

**R**Standard 2.1c: Combine Functions by Composition.
Modeling refers to actually being able to translate the equation into a visual picture. Writing a linear equation requires a person to understand how letters (called variables) interact with numbers by operations. Solving these problems involves finding the number that makes the equation true. These linear equations are actually lines on a coordinate plane. There are several ways to solve these types problem.

Example Problems for Standard 2.1c
Below are two example problems.

If f(x)=2x+5 and g(x)=3x,what is the value of (f° g)(1)?
 * Problem 1:**

11 because f(x)=2x+5 G(x)=3x (f° g)(1) (f° g)(1)=2(3x)+5 (f° g)(1)=6x(1)+5=11

To answer this question, you must understand what the equation is stating. It is saying a number is multiplied to 4. This answer is then subtracted by 10 and the result is 18. In order to find the number, we must complete inverse operations. This means completing the opposite operation and working in reverse. See the steps below.

The answer is 11 because: f(x)=2x+5 G(x)=3x Steps: replace the x with a 1 (f° g)(1) simplify f(x) and G(x) by adding them together; 2x+5 and 3x (f° g)(1)=2(3x)+5 now that you have simplified; multiply the problem; 2(3x) (f° g)(1)=6x+5 Now back to the x, replace it with a 1 which will get you (f° g)(1)=6(1)+5 Finally you will multiply the 6(1), then add 6+5=11 6+5 (f° g)(1)= 11

(f° g)(1)=6x(1)+5=11

f(x)=2x+7g(x)=3x -1 What is f(g(x))?
 * Problem 1 -**

f(x)=2x+7g(x)=3x -1 What is f(g(x))?

This question is only difficult because it is asking you to create an equation. It also is a word problem which is often harder for most students. In order to answer this question, think about what operations you have to use to get how much Stacy earns. This helps to create the equation. Well, Stacy makes 15 a week to start. But she also gets .50 for each customer. Well, to find out how much she gets if she had 10 customers, we would multiply .50 by 10 customers. We still would have to add 15 to get her amount. Let's see, we multiplied and added. Let's write an equation in words then replace the words with letters and numbers.

Stacy's weekly pay = .50 x customers + 15 $25 = .50c + 15

Podcast for Standard 1.1a
Below is a tutorial on understanding two-step equations and how to solve the problems.