46,47&49 | Relations, Functions and Graphs | Multiple Choice 6 | CXC CSEC Mathematics
CXC CSEC Mathematics Multiple Choice 6 – In this Caribbean Examination Council (CXC) Caribbean Secondary Education Certificate (CSEC) Mathematics Multiple Choice Examination, questions 46, 47 and 49 are based on the topic Relations, Functions and Graphs.
Related videos:
Inequalities and number lines: • Inequations | Number Line | Algebra
This topic:
RELATIONS, FUNCTIONS AND GRAPHS (Playlist: • 9. Relations, Functions and Graphs )
Upon completion of this series of videos on this topic, you will understand/be able to:
1. explain basic concepts associated with relations;
a. Concept of a relation, types of relations, examples and non-examples of relations, domain, range, image, co-domain.
2. represent a relation in various ways;
a. Set of ordered pairs, arrow diagrams, graphically, algebraically.
3. state the characteristics that define a function;
a. Concept of a function, examples and non-examples of functions.
4. use functional notation;
a. For example, (𝑥) = 𝑥2 as well as 𝑦 = (𝑥) for given domains. The inverse function 𝑓−1(𝑥). Composite functions 𝑓𝑔 = 𝑓(𝑔(𝑥))
5. distinguish between a relation and a function;
a. Ordered pairs, arrow diagram, graphically (vertical line test).
6. draw graphs of linear functions;
a. Concept of linear function, types of linear function (𝑦 = 𝑐; 𝑥 = 𝑘; 𝑦 = 𝑚𝑥 + 𝑐; where 𝑚, and 𝑘 are real numbers).
7. determine the intercepts of the graph of linear functions;
a. 𝑥-intercepts and 𝑦-intercepts, graphically and algebraically.
8. determine the gradient of a straight line;
a. Definition of gradient/slope.
9. determine the equation of a straight line;
Using:
a. the graph of the line;
b. the co-ordinates of two points on the line;
c. the gradient and one point on the line;
d. one point on the line or its gradient, and its relationship to another line.
10. solve problems involving the gradient of parallel and perpendicular lines;
11. determine from co-ordinates on a line segment: (a) the length; and, (b) the co-ordinates of the midpoint;
a. The concept of magnitude or length, concept of midpoint.
12. solve a pair of simultaneous linear equations in two unknowns graphically;
a. Intersection of graphs.
13. represent the solution of linear inequalities in one variable using:
a. set notation;
b. the number line; and,
c. graph.
14. draw a graph to represent a linear inequality in two variables;
15. use linear programming techniques to graphically solve problems involving two variables;
16. derive the composition of functions;
a. Composite function of no more than two functions, for example, 𝑓𝑔, 𝑓2 given 𝑓 and 𝑔.
b. Non-commutativity of composite functions (𝑓𝑔 ≠ 𝑔𝑓) in general.
17. state the relationship between a function and its inverse;
a. The concept of the inverse of a function;
b. The composition of inverse functions (𝑥) and 𝑓−1(𝑥) is commutative and results in 𝑥.
18. derive the inverse of a function;
a. 𝑓−1,(𝑓𝑔)−1
19. evaluate a function 𝑓(𝑥) at a given value of 𝑥
a. (𝑎),−1(𝑎),𝑓𝑔(𝑎), where 𝑎 ∈ ℝ.
20. draw and use the graph of a quadratic function to identify its features: (a) an element of the domain that has a given image; (b) the image of a given element in the domain; (c) the maximum or minimum value of the function; and, (d) the equation of the axis of symmetry;
a. Roots of the equation
21. interpret the graph of a quadratic function to determine: (a) the interval of the domain for which the elements of the range may be greater than or less than a given point; (b) an estimate of the value of the gradient at a given point; (c) intercepts of the function;
a. Concepts of gradient of a curve at a point, tangent, turning point. Roots of the function.
22. determine the equation of the axis of symmetry and the maximum or minimum value of a quadratic function expressed in the form 𝑎(𝑥 + ℎ)2 + 𝑘;
23. sketch the graph of a quadratic function expressed in the form 𝑦 = 𝑎(𝑥 + ℎ)2 + 𝑘 and determine the number of roots;
24. draw graphs of non-linear functions;
a. 𝑦 = 𝑎𝑥𝑛 where 𝑛 = −1,−2 and + 3 and 𝑎 is a constant.
b. Including distance-time and speed-time.
25. interpret graphs of functions; and,
a. Including distance-time graphs and speed-time graphs.
26. solve problems involving graphs of linear and non-linear functions.
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