4.1 Functions

• Relations and types of mappings: one-to-one, many-to-one, one-to-many, many-to-many
• Function notation and evaluation of functions; domain and range
• Types of function: algebraic functions only (polynomials and rational functions)
• Inverse functions: linear polynomials, a polynomial on a restricted domain, and inverse trigonometric ratios
• Limits of polynomials, and applications of functions to real-life situations

• identify relations and the different types of mappings
• identify functions and their properties
• determine the range and domain of functions
• compute the value of a function in different situations
• determine the inverse of a function of polynomials and trigonometric ratios
• evaluate limits of polynomial functions in different situations
• apply functions to real life situations
• appreciate the use of functions in real life situations

“How are functions applied in daily life?”

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1. Relations and mappings
   40 min · 1 practice tasks · quiz
   Classify a relation as one-to-one, many-to-one, one-to-many or many-to-many, and keep only the mappings that give each input one output.
2. Function notation and values
   40 min · 1 practice tasks · quiz
   Read f(x) as the output for the input x, and evaluate a polynomial and a simple rational function, including a fare rule.
3. Domain and range
   40 min · 1 practice tasks · quiz
   State the allowed inputs and the outputs actually obtained for a square, a reciprocal and a fare.
4. Polynomials and rational functions
   40 min · 1 practice tasks · quiz
   Identify polynomials by degree and rational functions by a denominator, and find one rational range by rearranging.
5. Inverse of a linear function
   40 min · 1 practice tasks · quiz
   Undo a linear polynomial by reversing its steps, and see why a many-to-one square has no inverse on all real numbers.
6. A restricted inverse, and trig ratios
   40 min · 1 practice tasks · quiz
   Invert a square on non-negative side lengths, and use principal values so each sine, cosine or tangent ratio has one angle.
7. Limits of polynomials
   40 min · 1 practice tasks · quiz
   See a polynomial settle on a value as x approaches a number, then find that limit by substitution.
8. Functions in a fare, a tank and a shamba
   40 min · 1 practice tasks · quiz
   Evaluate a fare, a draining tank and a rectangular plot, state each domain, and undo the fare and the plot.