Classification of Functions Quiz

Classification of Functions

• Functions can be classified into three types: one-to-one correspondence, one-to-many correspondence, and many-to-one correspondence.
• In a function machine, the input represents the independent variable while the output is the dependent variable.

Real-Life Function Representations

• Total salary (S) for a person earning ₱750.00 per day can be expressed as:
  S(n) = 750n, where n is the number of days worked.
• Rental fee (R) for a computer shop charging ₱15.00 per hour can be represented as:
  R(t) = 15t, where t is the number of hours rented.
• For a tricycle ride, the fare (F) can be expressed as a piecewise function:
  F(d) = { 10, if d ≤ 2
  10 + 8(d - 2), if d > 2 }
  Here, d represents the distance in kilometers.

Evaluating Functions

• Functions can be evaluated by substituting the variable with specific values from the domain.
• Example evaluation: Determine Kevin's savings for a specific number of days.

Understanding Relations and Functions

• A relation is a set of ordered pairs, and the domain consists of the first elements while the range consists of the second elements.
• For a relation to be classified as a function, each domain element must correspond to exactly one range element.
• Examples of ordered pairs:
  • Relation A = {(1,2), (2,3), (3,4), (4,5)} is a function.
  • Relation B = {(3,3), (4,4), (5,5), (6,6)} is also a function.
  • Relation C = {(1,0), (0,1), (-1,0), (0,-1)} is not a function because 0 corresponds to two different outputs.
  • Relation D = {(a,b), (b,c), (c,d), (a,d)} is not a function due to repeated elements in the domain.

Graphical Representation and the Vertical Line Test

• A function can be illustrated using graphs in the Cartesian plane.
• The vertical line test states that a graph represents a function if any vertical line intersects it at exactly one point.
• Graph Examples:
  • Graphs A and C pass the vertical line test, indicating they are functions.
  • Graphs B and D fail the vertical line test, hence are not functions.

Multiple Representations of Functions

• Functions can be represented through various mediums: words, tables, mappings, equations, and graphs.
• Mathematical functions express a relationship where the output (y) depends on the input (x). For example, a function that adds three to the input can be denoted as y = x + 3.

Various Function Activities and Evaluations

• Activities include evaluating algebraic expressions and understanding real-life scenarios as functions.
• It is essential to practice evaluating functions and recognizing their applications in everyday situations.

Test your understanding of different types of functions and their representations in real-life scenarios. This quiz covers one-to-one, one-to-many, and many-to-one correspondences along with examples of salary and rental fees. Evaluate functions using provided formulas and piecewise functions.