Consider the function $$y = 8 \sin \frac { \pi x } { 8 }$$ on the interval $$[ 0,16 ]$$ . Determine the $$\chi$$ -intercepts by giving the $$\chi$$ -coordinate(s).
A) $$0,8,24$$
B) $$0,8,16$$
C) $$8,16$$
D) $$0,16$$
E) $$0,8 \pi , 16 \pi$$

Question

Quizplus · Accepted Answer

The x-intercepts of a function occur where the function equals zero. For the given function $y = 8 \sin \frac{\pi x}{8}$, setting $y = 0$ gives $\sin \frac{\pi x}{8} = 0$. The sine function equals zero at integer multiples of $\pi$, so we solve $\frac{\pi x}{8} = n\pi$, where $n$ is an integer. This gives $x = 8n$. Within the interval $[0,16]$, the values of $n$ that satisfy this are $n = 0, 1, 2$, leading to $x = 0, 8, 16$.

Consider the Function y=8sin⁡πx8y = 8 \sin \frac { \pi x } { 8 }y=8sin8πx​

Consider the Function $y = 8 \sin \frac { \pi x } { 8 }$