relations and functions worksheet grade 11

3 min read 23-11-2024

relations and functions worksheet grade 11

Meta Description: Conquer your Grade 11 math! This comprehensive worksheet covers relations and functions, including domain, range, types of functions, and practice problems with solutions. Master the concepts and boost your understanding with detailed explanations and examples. Perfect for homework or exam prep!

Understanding Relations and Functions

This worksheet will help solidify your understanding of relations and functions, essential concepts in Grade 11 mathematics. We'll explore key definitions, different types of functions, and provide ample practice problems to test your knowledge. Let's start with the basics:

What is a Relation?

A relation is simply a set of ordered pairs. These pairs can be represented in various ways: as a set of points, a table, a graph, or a mapping diagram. The key is that each ordered pair connects an input value (x) to an output value (y).

For example: {(1, 2), (3, 4), (5, 6)} is a relation.

What is a Function?

A function is a special type of relation where each input (x-value) has only one output (y-value). This is often described as the "vertical line test"—if a vertical line intersects a graph at more than one point, it's not a function.

Example of a Function: {(1, 2), (2, 4), (3, 6)} Each x-value has a unique y-value.

Example of a Relation that is NOT a Function: {(1, 2), (1, 3), (2, 4)} The x-value 1 has two different y-values.

Domain and Range

The domain of a relation or function is the set of all possible input values (x-values). The range is the set of all possible output values (y-values).

Example: For the function {(1, 2), (2, 4), (3, 6)}, the domain is {1, 2, 3} and the range is {2, 4, 6}.

Types of Functions

Several types of functions are commonly studied in Grade 11:

1. Linear Functions

These functions have the form f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept. Their graphs are straight lines.

Example: f(x) = 2x + 1

2. Quadratic Functions

These functions have the form f(x) = ax² + bx + c, where 'a', 'b', and 'c' are constants. Their graphs are parabolas.

Example: f(x) = x² - 3x + 2

3. Polynomial Functions

These are functions that can be expressed as a sum of powers of x, each multiplied by a constant. Linear and quadratic functions are special cases of polynomial functions.

Example: f(x) = x³ - 2x² + x - 1

4. Exponential Functions

These functions have the form f(x) = aᵇˣ, where 'a' and 'b' are constants. They model exponential growth or decay.

Example: f(x) = 2ˣ

5. Rational Functions

These are functions that can be expressed as the ratio of two polynomials.

Example: f(x) = (x + 1) / (x - 2)

Practice Problems

(Remember to show your work!)

Determine if the following relations are functions:

a) {(1, 2), (2, 4), (3, 6), (4,8)} b) {(1, 2), (1, 3), (2, 4)} c) {(1,1), (2,2), (3,3)}
Find the domain and range of the following functions:

a) f(x) = 2x + 1 for x ∈ {-1, 0, 1, 2} b) {(1, 2), (2, 4), (3, 6)} c) The graph of a parabola that opens upwards with a vertex at (1,-2)
Identify the type of function:

a) f(x) = 3x - 5 b) f(x) = x² + 2x - 3 c) f(x) = 2ˣ d) f(x) = (x+1)/(x-1)

Solutions to Practice Problems

a) Function b) Not a function c) Function
a) Domain: -1, 0, 1, 2}; Range {-1, 1, 3, 5 b) Domain: 1, 2, 3}; Range {2, 4, 6 c) Domain: all real numbers; Range: [-2, ∞)
a) Linear b) Quadratic c) Exponential d) Rational

This worksheet provides a foundational understanding of relations and functions. For further practice, consult your textbook or online resources. Remember that consistent practice is key to mastering these concepts! Good luck!