The function $$ f $$ is defined by $$ y=a \cos k(x-b) $$ or $$ y=a \sin k(x-b) $$, where $$ k0 $$ and $$ b \geq 0 $$. The function $$ g $$ is defined by $$ y= an c(x-d) $$, where $$ c0 $$ and $$ d0 $$. Use the graphs of $$ f $$ and $$ g $$ to answer the following question. If we consider the graph of $$ f $$ as a cosine curve in the $$ x $$-axis Which of the following will represent the equation of $$ f $$ ? Choose the correct option.

Question

The function $$ f $$ is defined by $$ y=a \cos k(x-b) $$ or $$ y=a \sin k(x-b) $$, where $$ k>0 $$ and $$ b \geq 0 $$. The function $$ g $$ is defined by $$ y=	an c(x-d) $$, where $$ c>0 $$ and $$ d>0 $$. Use the graphs of $$ f $$ and $$ g $$ to answer the following question. If we consider the graph of $$ f $$ as a cosine curve in the $$ x $$-axis Which of the following will represent the equation of $$ f $$ ? Choose the correct option.

UpStudy AI · Accepted Answer

To determine the correct equation for the function $$ f $$ defined as $$ y = a \cos k(x - b) $$ or $$ y = a \sin k(x - b) $$, we need to consider the characteristics of cosine and sine functions.

1. **Cosine Function**: The general form $$ y = a \cos k(x - b) $$ represents a cosine wave with:
   - Amplitude: $$ |a| $$
   - Period: $$ \frac{2\pi}{k} $$
   - Phase Shift: $$ b $$ (to the right if $$ b > 0 $$)

2. **Sine Function**: The general form $$ y = a \sin k(x - b) $$ represents a sine wave with:
   - Amplitude: $$ |a| $$
   - Period: $$ \frac{2\pi}{k} $$
   - Phase Shift: $$ b $$ (to the right if $$ b > 0 $$)

Given that you mentioned considering the graph of $$ f $$ as a cosine curve, we can conclude that the equation of $$ f $$ is likely in the form of the cosine function.

Thus, the correct representation of the equation of $$ f $$ is:

$$
y = a \cos k(x - b)
$$

If you have specific options to choose from, please provide them, and I can help you identify the correct one based on the information above.
The equation of $$ f $$ is $$ y = a \cos k(x - b) $$.

The function is defined by
or , where and .
The function is defined by
, where and .
Use the graphs of and to answer the following question.
If we consider the graph of as a cosine curve in the -axis
Which of the following will represent the equation of ?
Choose the correct option.

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The function is defined by or , where and . The function is defined by , where and . Use the graphs of and to answer the following question. If we consider the graph of as a cosine curve in the -axis Which of the following will represent the equation of ? Choose the correct option.