Question

Find the number of points of intersection of the graph
$y=x+1\forall x\in [-2\pi ,2\pi ]\&$
$f\left(x\right)=0.25\sin x.$

• A. 1

Answer 1

The correct option is A 1
Given: $y=x+1\forall x\in [-2\pi ,2\pi ]$ and $f\left(x\right)=0.25\sin x$
Now, the graph of $f\left(x\right)=0.25\sin x$ will be same as the graph of $\sin x$ but shrunked $0.25$ times vertically as shown:

Thus, for $x\in [-2\pi ,2\pi ],$ the function $f\left(x\right)=0.25\sin x$ and $y=x+1$ intersect each other at only one point.
$\therefore$ Number of points of Intersection $=1.$