Question

The graph of a function $y=a\cos bx+c$ is given below


Then, the function $y$ is

• A. $y=2\sin x+2$
• B. $y=3\sin x+1$
• C. $y=3\cos x+1$
• D. $y=2\cos x+2$

Answer 1

The correct option is D $y=2\cos x+2$

Graph of $y=f\left(x\right)$ has range $[0,4]$
Graph of $\frac{y}{2}$ will have range $[0,2]$
$\because \frac{y}{2}$ graph shrinks vertically $\frac{1}{2}$ times the graph of $y=f\left(x\right)$


Now, the graph of $\frac{1}{2}y-1$ will be


Which is the graph of $\cos x$ curve, so
$\frac{y}{2}-1=\cos x\Rightarrow y=2(\cos x+1)$