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 ((\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=(\max -\min )/(2) \\ =(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}=(\max +\min )/(2) \\ =(1+11)/(2) \\ =6 \end{gathered}`

Thus, the midline is correct.

Thus, option (b) is the solution.