Questions: Graf ktorej z nasledujúcich funkcií má na intervale ⟨0,2 π⟩ najviac priesečníkov s osou x ? (A) f1: y=2+sin x (B) f2: y=2 sin x (C) f3: y=sin (x/2) (D) f4: y=sin 2x (E) f5: y=sin x

Graf ktorej z nasledujúcich funkcií má na intervale ⟨0,2 π⟩ najviac priesečníkov s osou x ?
(A) f1: y=2+sin x
(B) f2: y=2 sin x
(C) f3: y=sin (x/2)
(D) f4: y=sin 2x
(E) f5: y=sin x

Transcript text: Graf ktorej $z$ nasledujúcich funkcií má na intervale $\langle 0,2 \pi\rangle$ najviac priesečníkov s osou $x$ ? (A) $f_{1}: y=2+\sin x$ (B) $f_{2}: y=2 \sin x$ (C) $f_{3}: y=\sin \frac{x}{2}$ (D) $f_{4}: y=\sin 2 x$ (E) $f_{5}: y=\sin x$

Solution

Solution Steps

To determine which function has the fewest intersections with the x-axis on the interval $\langle 0, 2\pi \rangle$, we need to find the number of roots (or zeros) of each function within this interval. A function intersects the x-axis where its value is zero. We will evaluate each function to find the number of such points.

Step 1: Identify the Functions

We are given five functions to analyze for their intersections with the x-axis on the interval $ \langle 0, 2\pi \rangle $: