QUESTION 5
In the diagram below, the graphs of 𝑓(𝑥) = 𝑎 𝑐𝑜𝑠 𝑏𝑥 and 𝑔(𝑥) = 𝑠𝑖𝑛(𝑥 + 𝑝) are drawn for 𝑥 ∈ [− 180°; 180°].
Figure 4: Diagram for question 5.
5.1
Write down the values of 𝑎, 𝑏 and 𝑝.
(3)
5.2
For which values of 𝑥 in the given interval does the graph of 𝑓 increase as the graph of 𝑔 increases?
(2)
5.3
Write down the period of 𝑓(2𝑥).
(2)
5.4
Determine the minimum value of h if h(𝑥) = 3 𝑓(𝑥) − 1.
(2)
5.5
Describe how the graph 𝑔 must be transformed to form the graph 𝑘, where 𝑘(𝑥) =− 𝑐𝑜𝑠 𝑥.
(2)
[11]
8
QUESTION 6
Given: 𝑓(𝑥) = 𝑡𝑎𝑛 𝑥 and 𝑔(𝑥) = 𝑠𝑖𝑛 2𝑥.
Draw the graphs of 𝑓 and 𝑔 for 𝑥 ∈ [− 90°; 180°] on the grid provided. Show all the turning points and intercepts with the axes.
Clearly show the asymptotes using dotted lines.
(6)
[6]
1 answer