Question

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. Anyone??​

Answer 1

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

`f(x)=2-(3x)/(4\pi) \implies f(0)=2,\quad f(2\pi)=(1)/(2)`

So, you just need to draw the points

`(0,2),\quad \left(2\pi, (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.