Function Notation Worksheet Overview

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Function notation is a way of representing a function using symbols and mathematical expressions. It is a useful tool in mathematics that allows for easier manipulation and calculation of functions. In this article, we will discuss function notation and provide a worksheet to practice using it.

Function notation is typically represented by the symbol “f(x)” or “g(x)”, where the letter inside the parentheses (in this case, “x”) represents the input of the function. For example, if we have a function f(x) = 2x + 3, this means that the function f takes an input x and outputs 2x + 3.

Using function notation, we can write the above function as f(5) = 2(5) + 3, which simplifies to f(5) = 13. This tells us that when the input is 5, the output of the function is 13.

Function notation is particularly helpful when working with multiple functions or when performing operations on functions. For example, if we have two functions, f(x) = 2x + 3 and g(x) = x^2, we can use function notation to represent the composite function f(g(x)). This means that we apply function g to the input x, and then apply function f to the output of g. In other words, f(g(x)) = f(x^2) = 2(x^2) + 3.

Function notation allows us to be more precise and concise in our mathematical expressions, and it makes it easier to understand and work with functions. To gain proficiency in using function notation, it is important to practice solving problems and exercises. Below is a worksheet containing various problems involving function notation. Try to solve each problem step by step, and use function notation whenever necessary.

Worksheet: Function Notation

1. Consider the function f(x) = 3x – 5. Find f(2).

2. Given the function g(x) = x^2 + 4x, find g(3).

3. Let h(x) = 2x^2 – x + 3. Determine h(4).

4. Suppose f(x) = x^3 + 2x – 1 and g(x) = 4x + 2. Find f(g(1)).

5. Given the functions f(x) = 2x + 1 and g(x) = 3x – 2, calculate f(g(2)).

6. Consider the function h(x) = x^2 – 3x. Calculate h(5).

7. Let f(x) = 3x – 4 and g(x) = x^2. Determine f(g(3)).

8. Given the functions f(x) = x^2 – 1 and g(x) = 2x, find g(f(2)).

9. Suppose h(x) = x^3 + 2x + 1. Calculate h(-1).

10. Consider the function f(x) = 4x – 7. Find f(-3).

Solutions:

1. f(2) = 3(2) – 5 = 6 – 5 = 1.

2. g(3) = 3^2 + 4(3) = 9 + 12 = 21.

3. h(4) = 2(4)^2 – 4 + 3 = 2(16) – 4 + 3 = 32 – 4 + 3 = 31.

4. f(g(1)) = f(4(1) + 2) = f(6) = 6^3 + 2(6) – 1 = 216 + 12 – 1 = 227.

5. f(g(2)) = f(3(2) – 2) = f(4) = 2(4) + 1 = 8 + 1 = 9.

6. h(5) = 5^2 – 3(5) = 25 – 15 = 10.

7. f(g(3)) = f(3^2) = f(9) = 3(9) – 4 = 27 – 4 = 23.

8. g(f(2)) = g(2^2 – 1) = g(3) = 2(3) = 6.

9. h(-1) = (-1)^3 + 2(-1) + 1 = -1 – 2 + 1 = -2.

10. f(-3) = 4(-3) – 7 = -12 – 7 = -19.

By practicing the problems in this worksheet, you will become more confident in using function notation and working with functions in general. Function notation is a valuable tool in mathematics that simplifies the representation and calculation of functions, making it easier to solve complex problems and analyze relationships between variables. Keep practicing and exploring different functions to enhance your skills and understanding of function notation.

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