## Mathematical presentations

For relations:Task I: PRESENTATION
f(x)=x2-2x-3
g(x)= 3x+1 h(x)=)- 3 i(x)=:+1 (1,3) (2,4) (1,5) (3,4)
x=6 1) Distinguish which relation is a function, and which relation is not a function through at least five different methods (k,t) (e.g.: table of values, mapping diagrams, graphs, vertical line test) (A 1.1)(2 p) 2) Determine the domain and range of each function through their graphs and algebraic representations and numeric relations (1st). Express the domain and range in appropriate way (k,c). If g(x) is used to model a population change with time, how would the domain and range of g(x) change (k,t)? (A1.3)(2 p) 3) Determine the inverse algebraic and numeric representations of each inverse operation (1c,t). Using graphing technology, tracing papers, and algebraic representation to figure out the connection between a function and its inverse (k,t). (A 1.5, 1.7) (2 p) 4) Determine the domain and range of each reverse through the graph and algebraic representations (k). Figure out if the reverse relation is a function (k,t). (A 1.6) (2 p) 5) If f(x) was transformed to f(x)= -3×2-3x+6, g(x) was transformed to
g(x)=0.5x+7, h(x) was transformed to h(x)= V30x+2, and i(x) was
transformed to i(x)=— -2 + 1, the transformation parameters x –
in y=af(k(x-d))+c through graphing technology (k,t,a). Describe the detailed transformation procedure (k,c). (A1.8) (2 p)
Task II Investigation A rock is thrown straight up in the air from an initial height ho with an initial velocity vo, in meters per second. The height in meters above the ground after t seconds is given by h(t)= – 4.9t2+vot+ho.
1) If vo=2m/s, ho=2m, determine the number of zeros of the function h(t) by at least three strategies (k,t). (A 2.1) (2 p)
2) Determine the maximum height through the function algebraic expression (k). (A 2.2, A 2.3 half) (2 p)
3) If vo=1.5m/s, ho=0.5 m, find an expression for the time it takes the rock to reach its maximum height (k,a). (A 2.3) (2 p)
4) If a. vo=29.4m/s, ho=24.5m
What’s the transformation relationship between the three functions (k,t)? If the zero points of the function of h(t) is 0 and 9, and the graph of the function goes through the point (7, 8.5), what is the algebraic expression ofh(t) (k,a)? (A 2.4) (2 p)
5) Suppose h(t)=-4.9t2+27t+23, if a bird fly in the route of a function f(t) =5x+7. Will the bird be hit by the rock? Solve this problem by sketching the graph and through algebraic representation. (k,t,a)(A 2.5) (2 p)
1. This task is individual task. Evaluation would be performed individually based on teacher’s observation and your hand-in product.
2. Students are allowed to use in-class material only to solve the question effectively.
3. Each student is required to hand in a printable answer sheet. The sheet should include the process of demonstration and question solving procedure.
4. Each student need to make a brief presentation at the end of this task. You performance will be evaluated.
5. This task is 15 marks in total, including: Hand-in answer sheet, presentation, and teacher’s observation.
The regional municipality of Wood Buffalo, Alberta, has experienced a large population increase in recent years due to the discovery of one of the world’s largest oil deposit. Its population, 35000 in 1996, has grown at an annual rate of approximately 8%.
Time (year 0 from 1996)
1 2 3 4 5 6 7 3 9
Population 35.0 (thousands)
37.8 40.8 44.1 47.6 MA 55.5 60M 64.8 70M
1) Sketch the data in the table of value, and graph it using graphing calculator or
graphing software (k,a). Explain what kind of function it is. Evaluate the function (k,c).(B1.1, B 3.2half) (4 p)
2) Through the graph and the algebraic expression of the function, describe the domain and range, intercepts, increasing and decreasing interval, and asymptotes for the function of population (k,c). (B 1.4, B3 .2half) (4 p)
3) If the function is transformed by y=af(k(x-d))+c. a=1, k=2, d=0.8, c=1000. What will be the new function (k,t)? Use graphing calculator sketch the new function. Explain the roles of the four parameters (k,c). (B2.2) (3 p)