Question

Choose the function whose graph is given by:

Answer 1

Answer:

$y=3sec\left(\frac{1}{2}x\right)$

Step-by-step explanation:

The graphs of $sec(x)$ can be obtained from  the graph of the cosine function using the reciprocal identity, so:

$sec(x)=\frac{1}{cos(x)}$

But in this problem, the graph stands for the function:

$y=3sec\left(\frac{1}{2}x\right)$

Because the period is now 4π as indicated and for $x=0$ in the figure and this can be proven as follows:

$Period=\frac{2\pi}{\frac{1}{2}}=4\pi$

Also, $for \ x=1 \ then \ y=3$ as indicated in the figure and this can be proven as:

$y=3sec\left(\frac{1}{2}x\right) \\ \\ y=\frac{3}{cos(0.5x)} \\ \\ y=\frac{3}{cos(0.5(0))} \\ \\ y=\frac{3}{1}=3$