Question

How do you graph $y=-\dfrac{1}{2}\cos x$ ?

Answer 1

To graph the given function $y=-\dfrac{1}{2}\cos x$, first of all, we are going to draw the graph of $\cos x$ and then multiply the negative of 1 with $\cos x$. When we multiply the negative of 1 with $\cos x$ then we have to take the mirror image of the graph of $\cos x$ in the line mirror present on the x axis. Now, we will multiply one half to $-\cos x$ then we have to shrink the y value of the graph of $-\cos x$ by one half.

Complete step-by-step answer:
The function given in the above problem which we have to graph is as follows:
$y=-\dfrac{1}{2}\cos x$
To draw the above function on the graph paper, first of all, we are going to draw $\cos x$ on the graph. In the below, we have drawn the graph of $\cos x$.

Now, we are going to draw the graph of $-\cos x$ by taking the mirror image of the above graph in the line mirror placed at x axis.

The dotted line in the above graph is the mirror image of $\cos x$ in the line mirror of x axis so the dotted line pink graph above is of $-\cos x$.
Now, we are drawing the graph of $-\dfrac{1}{2}\cos x$ by shrinking all the y values of the above graph by $\dfrac{1}{2}$.

In the above graph, as you can see that the y value of the blue curve is lesser than that of the dotted pink curve so the blue curve is the graph of $-\dfrac{1}{2}\cos x$.
Now, we are eliminating the pink dotted curve from the above graph then we get,

Hence, we have drawn the graph of $y=-\dfrac{1}{2}\cos x$ which is shown below:

Note: The mistake that could be possible in the drawing of the above graph is that when converting graph from $\cos x$ to $-\cos x$, you will take the mirror image of the graph in the line mirror placed on the y axis because you think that all the y values are changing so line mirror should present on the y axis. But this is the wrong way of conversion from $\cos x$ to $-\cos x$ so make sure you won’t make this mistake in the exam.