Respuesta :
Substitute 0 for x in the function y = 2 cos (4x) + 1 to determine the point at which function intersect the y-axis.
[tex]\begin{gathered} y=2\cos (4\cdot0)+1 \\ =2\cdot1+1 \\ =3 \end{gathered}[/tex]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.
[tex]\begin{gathered} 0=2\cos (4x)+1 \\ \cos (4x)=-\frac{1}{2} \\ 4x=\frac{2\pi}{3},\frac{4\pi}{3} \\ x=\frac{\pi}{6},\frac{\pi}{3} \end{gathered}[/tex]So points at which function intersect the x axis is,
[tex](\frac{\pi}{6},0)\text{ and (}\frac{\pi}{3},0)[/tex]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
