5.1
𝑎 = 1, 𝑏 = 1, 𝑝 = 90°
5.2
The graph of 𝑓 increases as the graph of 𝑔 increases for 𝑥 ∈ [0°; 90°] and 𝑥 ∈ [180°; 270°].
5.3
The period of 𝑓(2𝑥) is 90°.
5.4
The minimum value of h is -1.
5.5
The graph 𝑔 must be reflected about the x-axis to form the graph 𝑘.
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)
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1 answer