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:

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

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.