Function Composition Common Core Algebra 2 Homework Answer Key Introduction:
As you delve deeper into the concepts of algebra, function composition is an inevitable topic you will come across. However, this topic can be confusing and challenging for students who are still new to this field. Therefore, in this blog post, we will dive deep into the world of function composition in Common Core Algebra 2 and provide you with a homework answer key to help you streamline your learning process. So let’s get started!
The concept of function composition is relatively simple – it is the process of evaluating one function inside another function. To understand it better, let’s take a look at an example. Suppose we have two functions, f(x) = x + 1 and g(x) = 2x. We can take the function g and plug it into the function f as follows: f(g(x)). This means that we are taking the output of function g and plugging it into function f.
Now, how do we evaluate this composition? Let’s use the above example and evaluate f(g(3)). Firstly, we need to plug the value of x (which is 3) into function g. Therefore, g(3) = 2(3) = 6. Next, we take the output of g(3) (which is 6) and plug it into function f. Therefore, f(6) = 6 + 1 = 7. Hence, f(g(3)) = 7.
While this concept may seem simple, it can be challenging when dealing with more complex functions. However, there are some shortcuts that can help us to evaluate the composition of functions easily. One such shortcut is the use of a composition chart. The chart helps us break down the composition into smaller steps, making it easier to evaluate.
Now that we have covered the basics of function composition, let’s dive into some practice problems. Here is a homework answer key for some of the problems you may encounter in your Common Core Algebra 2 course:
- f(x) = 2x + 1 and g(x) = 3x – 4. Find f(g(5)).
Solution: First, find g(5) = 3(5) – 4 = 11. Next, find f(11) = 2(11) + 1 = 23. Therefore, f(g(5)) = 23.
- h(x) = x – 1 and k(x) = x^2. Find h(k(t + 1)).
Solution: First, find k(t + 1) = (t + 1)^2 = t^2 + 2t + 1. Next, find h(t^2 + 2t) = (t^2 + 2t) – 1 = t^2 + 2t – 1. Therefore, h(k(t + 1)) = t^2 + 2t – 1.
- p(x) = 4x and q(x) = x – 5. Find p(q(x)).
Solution: First, find q(x) = x – 5. Next, find p(x – 5) = 4(x – 5) = 4x – 20. Therefore, p(q(x)) = 4x – 20.
Function composition is a critical topic in Common Core Algebra 2, and it is crucial to understand the concept thoroughly. By using the homework answer key provided in this blog post, you can practice solving various problems related to function composition and strengthen your understanding of this topic. Remember, practice makes perfect, so keep practicing until you feel confident enough to tackle any problem!