Question

Select the graph of y = 2 cos (4x) +1.TTEN-1O-2++++++++++بنof

Answer 1

Substitute 0 for x in the function y = 2 cos (4x) + 1 to determine the point at which function intersect the y-axis.

`\begin{gathered} y=2\cos (4\cdot0)+1 \\ =2\cdot1+1 \\ =3 \end{gathered}`

So curve function intersect the y-axis at (0,3).

Substitute 0 for y in the equation to determine the point at which function intersect the x-axis.

`\begin{gathered} 0=2\cos (4x)+1 \\ \cos (4x)=-(1)/(2) \\ 4x=(2\pi)/(3),(4\pi)/(3) \\ x=(\pi)/(6),(\pi)/(3) \end{gathered}`

So points at which function intersect the x axis is,

`((\pi)/(6),0)\text{ and (}(\pi)/(3),0)`

So option D represents the correct graph, in which graph intersect the y axis at (3,0) and x axis at points (pi/6,0) and (pi/3,0). The graph intersect x axis at more than two points.

Answer: Option D