Question

identify the equation for this graph. f(x) = cos(x) f(x) = sin(x) f(x) = x² f(x) = |x|

Explanation:

Step1: Check key point (x=0)

For $f(x)=\cos(x)$, $f(0)=\cos(0)=1$; for $f(x)=\sin(x)$, $f(0)=\sin(0)=0$; for $f(x)=x^2$, $f(0)=0$; for $f(x)=|x|$, $f(0)=0$. The graph intersects the y-axis at $(0,1)$.

Step2: Verify curve shape

The graph is a periodic wave, matching trigonometric functions. $f(x)=x^2$ is a parabola, $f(x)=|x|$ is a V-shape, so they are eliminated. The y-intercept confirms it is not $f(x)=\sin(x)$.

Answer:

f(x) = cos(x)