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svlad2 [7]
3 years ago
11

This is a question I have been trying to do for quite a while. My additional mathematics exam is next week and I need help. Anyo

ne??​

Mathematics
1 answer:
Radda [10]3 years ago
3 0

First of all, let's consider the line, since it's simpler to graph: we draw the endpoints and connect them:

f(x)=2-\dfrac{3x}{4\pi} \implies f(0)=2,\quad f(2\pi)=\dfrac{1}{2}

So, you just need to draw the points

(0,2),\quad \left(2\pi, \dfrac{1}{2}\right)

As for the trigonometric function, we have to start from the parent function y=\sin(x) and derive the graph of its child function via transformations:

  • When we multiply the whole function by 2, we stretch the graph vertically. So, the function has still period 2\pi, but now it ranges from -2 to 2 instead of from -1 to 1 (amplitude 2)
  • When we multiply the argument by 2, we compress the function horizontally. So, the new period becomes \pi, and the function makes two complete oscillations from 0 to 2\pi

You can see the two functions in the image below. You can also see that the two graphs cross 4 times, meaning that the equation

y_1=y_2 has four solutions.

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