Question

Identify the function in the graph. (1 point) Responses f(x)=cos(8x) f left parenthesis x right parenthesis equals cosine left parenthesis 8 x right parenthesis f(x)=sin(8x) f left parenthesis x right parenthesis equals sine left parenthesis 8 x right parenthesis f(x)=sin(x8) fsine left parenthesis Start Fraction x over 8 End Fraction right parenthesis f(x)=cos(4x)

Answer 1

To identify the function based on the graph, you would need to look for specific characteristics, such as the frequency, amplitude, and general shape of the graph.

• If the graph is oscillating between -1 and 1 with a period of $\frac{2\pi }{8}=\frac{\pi }{4}$, then it is likely a cosine or sine function with an angular frequency of 8.

• If the function appears to start at its maximum value (when $x=0$), it would be a cosine function:

  • $f(x)=\cos (8x)$ or $f(x)=\cos (4x)$ based on their respective frequencies.

• If the function starts at zero and goes up, it would be a sine function:

  • $f(x)=\sin (8x)$ or $f(x)=\sin (x8)$ (though mathematically these are equivalent).

Given the options:

1. $f(x)=\cos (8x)$
2. $f(x)=\sin (8x)$
3. $f(x)=\sin (x8)$
4. $f(x)=\cos (4x)$

Without the actual graph, if you can note its behavior around $x=0$ and the period, that would help identify the correct function. If the graph is periodic with a shorter wavelength (indicating a higher frequency), it is likely $f(x)=\cos (8x)$ or $f(x)=\sin (8x)$.

In conclusion, if the graph looks like a cosine function starting at its peak, then choose $f(x)=\cos (8x)$. If it's a sine function starting at zero, choose $f(x)=\sin (8x)$.