A function is a mathematical term that refers to a particular type of relationship between two sets; one called the domain, the other the range. It is important to be familiar with the terminology of functions; the set of inputs into the function is referred to as the domain, the set of outputs is the range and the set of possible outputs is the co-domain. Functions link together learning from the strands of number, algebra and geometry, you are expected to be able to work with both linear and quadratic functions. This will involve interpreting graphs, plotting points and lines, drawing graphs, finding intersection points and interpreting the results.
Sample question 1
Two diagrams, labelled A and B, are shown below. One diagram represents a function; the other does not.
State which diagram does not represent a function. Justify your answer.
Diagram B does not represent a function as the first element in the inputs of diagram B has two possible outputs. For a relationship to be a function every element in the domain is mapped to one element in the co-domain.
Sample question 2
(i)Draw the graph of the function f:x ➝ x2 - 2x + 4 in the domain -2 ≤ x ≤ 4, where x ϵ R
The function f:x ➝ x2 - 2x + 4 gives the predicted wind speed, in km per hour, over a 6-hour period of time. The x-axis represents the time from 10 p.m. (x = -2) to 4 a.m. (x = 4).
Use your graph from (i) to answer the following questions. Show your work on the graph.
(ii)What is the predicted wind speed at midnight?
(iii)Find the times when the predicted wind speed is 5.5 km per hour.
See diagram. 11:25 pm and 2:35 am
(iv)If the wind speed is between 1.1 km per hour and 5.5 km per hour, it is called light air. According to your graph, for how long will the wind be light air?
3 hours and 10 minutes