Question

Q7Which statement is incorrect for the graph of thefunction y = -5 cosGcos( 3 (x – 3)) +62The period is 4.The amplitude is 3.The range is [1, 11].The midline is 6.

Answer 1

The given function is,

$y=-5\cos (\frac{\pi}{2}(x-3))+6$

The graph can be drawn as,

The period will be distance between two consequetive maximas,

$\text{Period}=1-(-3)=4$

Thus, period is correct.

The amplitude can be determined as,

$\begin{gathered} Amplitude=\frac{\max -\min }{2} \\ =\frac{11-1}{2} \\ =5 \end{gathered}$

Thus, amplitue is incorrect.

The range is,

$y\in\lbrack1,11\rbrack$

Thus, the range is correct.

The midline is,

$\begin{gathered} \text{midline}=\frac{\max +\min }{2} \\ =\frac{1+11}{2} \\ =6 \end{gathered}$

Thus, the midline is correct.

Thus, option (b) is the solution.