Function Notation Worksheet Answers Explained

Understanding Function Notation

Function notation is a way of describing a function using symbols and notation. It’s a fundamental concept in mathematics, and it’s used to express relationships between variables. In this post, we’ll explore function notation, provide a worksheet with answers, and explain the solutions in detail.

What is Function Notation?

Function notation is a way of expressing a function as a mathematical expression. It typically consists of a function name, followed by parentheses containing one or more input variables. The function name is usually a letter or a combination of letters, and the input variables are the values that are plugged into the function to produce an output.

For example, the function notation f(x) represents a function named f that takes one input variable x. The output of the function is denoted by f(x), which is read as “f of x”.

Worksheet: Function Notation

Here are some function notation problems for you to try. We’ll provide the answers and explanations later in this post.

Problem 1: If f(x) = 2x + 1, find f(3).

Problem 2: If g(x) = x^2 - 4, find g(-2).

Problem 3: If h(x) = 3x - 2, find h(0).

Problem 4: If j(x) = x^3 + 2, find j(1).

Problem 5: If k(x) = 2x^2 + 3x - 1, find k(2).

Answers and Explanations

Now, let’s go through the answers and explanations for each problem.

Problem 1: f(x) = 2x + 1, find f(3)

To find f(3), we need to substitute x = 3 into the function f(x) = 2x + 1. This gives us:

f(3) = 2(3) + 1 = 6 + 1 = 7

Therefore, f(3) = 7.

Problem 2: g(x) = x^2 - 4, find g(-2)

To find g(-2), we need to substitute x = -2 into the function g(x) = x^2 - 4. This gives us:

g(-2) = (-2)^2 - 4 = 4 - 4 = 0

Therefore, g(-2) = 0.

Problem 3: h(x) = 3x - 2, find h(0)

To find h(0), we need to substitute x = 0 into the function h(x) = 3x - 2. This gives us:

h(0) = 3(0) - 2 = 0 - 2 = -2

Therefore, h(0) = -2.

Problem 4: j(x) = x^3 + 2, find j(1)

To find j(1), we need to substitute x = 1 into the function j(x) = x^3 + 2. This gives us:

j(1) = (1)^3 + 2 = 1 + 2 = 3

Therefore, j(1) = 3.

Problem 5: k(x) = 2x^2 + 3x - 1, find k(2)

To find k(2), we need to substitute x = 2 into the function k(x) = 2x^2 + 3x - 1. This gives us:

k(2) = 2(2)^2 + 3(2) - 1 = 8 + 6 - 1 = 13

Therefore, k(2) = 13.

Conclusion

Function notation is a powerful tool for expressing relationships between variables. By understanding how to read and write function notation, you can solve a wide range of problems in mathematics, science, and engineering. Remember to substitute the input values into the function to find the output values, and don’t be afraid to ask for help if you get stuck.

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