Question

From the given graph if $f\left(x\right)=\cos x,$
then $g\left(x\right)=$

• A. $-\cos x-2$
• B. $\cos x-2$
• C. $\cos x+2$
• D. $\cos x+2$

Answer 1

The correct option is A $-\cos x-2$

Given the graph of $f\left(x\right)=\cos x$ and $g\left(x\right)$ as:

For the function $g\left(x\right):$
The function ranges from $-3\text{to}-1$ and is the opposite extreme of $\cos x$ i.e.
Wherever $\cos x=1$ the function $g\left(x\right)=-3$ and where $\cos x=-1,$ then $g\left(x\right)=-1.$
That means $g\left(x\right)$ is some transformed version of $-\cos x$
Now, the graph of $-\cos x$ can be drawn as:
Now, the function $g\left(x\right)$ ranges from $-1\text{to}-3$
Shifting the graph vertically downward by $2$ units, we get the graph of $-\cos x-2$ as:
Which is the required graph of $g\left(x\right)$
$\Rightarrow g\left(x\right)=-\cos x-2$