QUESTION 1 1.1 By completing the table below, draw the graphs of the following evven functions on the same set of axes provided where $$ x \in\left[0^{\circ} ; 360^{\circ} ight] $$. Label your graphe clearly by shownite the turning points, $$ x $$-intercepts and the $$ y $$-intereepts. The graphs of a stowld be axes b) $$ f(x)=\cos (x) $$ and $$ g(x)=3 \cos (x) $$ and $$ h(x)=\cos (3 x) $$. \begin{tabular}{|c|c|c|} \hline$$ x^{\circ} $$ & $$ 0^{\circ} $$ \ \hline $$ \sin (x) $$ \ \hline \end{tabular}

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QUESTION 1 1.1 By completing the table below, draw the graphs of the following evven functions on the same set of axes provided where $$ x \in\left[0^{\circ} ; 360^{\circ}ight] $$. Label your graphe clearly by shownite the turning points, $$ x $$-intercepts and the $$ y $$-intereepts. The graphs of a stowld be axes b) $$ f(x)=\cos (x) $$ and $$ g(x)=3 \cos (x) $$ and $$ h(x)=\cos (3 x) $$. \begin{tabular}{|c|c|c|} \hline$$ x^{\circ} $$ & $$ 0^{\circ} $$ \ \hline $$ \sin (x) $$ \ \hline \end{tabular}

UpStudy AI · Accepted Answer

It seems that I am unable to plot the graphs directly. However, I can guide you on how to plot the functions using graphing software or a graphing calculator.

### Instructions for Plotting

1. **Set Up the Axes**:
   - Create a Cartesian coordinate system with the x-axis ranging from $$ 0^{\circ} $$ to $$ 360^{\circ} $$.
   - The y-axis should be set to accommodate the values of $$ f(x) $$, $$ g(x) $$, and $$ h(x) $$. For $$ g(x) $$, the range should be from $$ -3 $$ to $$ 3 $$.

2. **Plotting the Functions**:
   - **For $$ f(x) = \cos(x) $$**:
     - Plot the points: $$ (0, 1) $$, $$ (90, 0) $$, $$ (180, -1) $$, $$ (270, 0) $$, $$ (360, 1) $$.
     - Connect these points smoothly to form the cosine wave.

- **For $$ g(x) = 3 \cos(x) $$**:
     - Plot the points: $$ (0, 3) $$, $$ (90, 0) $$, $$ (180, -3) $$, $$ (270, 0) $$, $$ (360, 3) $$.
     - Connect these points smoothly to form the scaled cosine wave.

- **For $$ h(x) = \cos(3x) $$**:
     - Plot the points: $$ (0, 1) $$, $$ (90, 0) $$, $$ (180, -1) $$, $$ (270, 0) $$, $$ (360, 1) $$.
     - This function will oscillate more frequently, so ensure to connect the points smoothly.

3. **Labeling**:
   - Clearly label each graph with its corresponding function name.
   - Mark the turning points, $$ x $$-intercepts, and $$ y $$-intercepts on the graph.

### Summary of Key Points
- **Turning Points**:
  - $$ f(x) $$ and $$ h(x) $$ have turning points at $$ (0, 1) $$, $$ (180, -1) $$, and $$ (360, 1) $$.
  - $$ g(x) $$ has turning points at $$ (0, 3) $$, $$ (180, -3) $$, and $$ (360, 3) $$.

- **$$ x $$-intercepts**:
  - All functions have $$ x $$-intercepts at $$ (90, 0) $$ and $$ (270, 0) $$.

- **$$ y $$-intercepts**:
  - $$ f(x) $$ and $$ h(x) $$ have $$ y $$-intercept at $$ (0, 1) $$.
  - $$ g(x) $$ has $$ y $$-intercept at $$ (0, 3) $$.

By following these instructions, you should be able to create a clear and informative graph of the functions $$ f(x) $$, $$ g(x) $$, and $$ h(x) $$. If you have any further questions or need additional assistance, feel free to ask!
To graph the functions $$ f(x) = \cos(x) $$, $$ g(x) = 3 \cos(x) $$, and $$ h(x) = \cos(3x) $$ over $$ x \in [0^{\circ}, 360^{\circ}] $$, follow these steps: 1. **Calculate Key Points**: - For $$ f(x) $$: - $$ 0^{\circ} $$: 1 - $$ 90^{\circ} $$: 0 - $$ 180^{\circ} $$: -1 - $$ 270^{\circ} $$: 0 - $$ 360^{\circ} $$: 1 - For $$ g(x) $$: - $$ 0^{\circ} $$: 3 - $$ 90^{\circ} $$: 0 - $$ 180^{\circ} $$: -3 - $$ 270^{\circ} $$: 0 - $$ 360^{\circ} $$: 3 - For $$ h(x) $$: - $$ 0^{\circ} $$: 1 - $$ 90^{\circ} $$: 0 - $$ 180^{\circ} $$: -1 - $$ 270^{\circ} $$: 0 - $$ 360^{\circ} $$: 1 2. **Plot the Graphs**: - Draw the x-axis from $$ 0^{\circ} $$ to $$ 360^{\circ} $$. - Draw the y-axis to accommodate values up to 3 for $$ g(x) $$. - Plot the points for each function and connect them smoothly. - Label each graph with its function name. - Mark turning points at $$ (0,1) $$, $$ (180,-1) $$, and $$ (360,1) $$ for $$ f(x) $$ and $$ h(x) $$, and at $$ (0,3) $$, $$ (180,-3) $$, and $$ (360,3) $$ for $$ g(x) $$. - Mark $$ x $$-intercepts at $$ (90,0) $$ and $$ (270,0) $$ for all functions. - Mark $$ y $$-intercept at $$ (0,1) $$ for $$ f(x) $$ and $$ h(x) $$, and at $$ (0,3) $$ for $$ g(x) $$. By following these steps, you can accurately graph the given functions and identify their key features.

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