Consider the function 𝑔(𝑥)=−2cos(2𝑥+180)−1&nbsp;a) State the parent function. [1T]&nbsp;b) Write the function in proper transformation form. [1T]&nbsp;c) Describe the transformations for all parameters, a, k , d and c. [4T]&nbsp;d) Create a transformation table/image table for the function and graph the function. [4A]&nbsp;d) The value for the y – intercept (use algebraic method). [1A]&nbsp;e) The value for the first 2 x – intercept(s) (use algebraic method) between 0°≤𝑥 ≤360° [2T]&nbsp;&nbsp;

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Consider the function 𝑔(𝑥)=−2cos(2𝑥+180)−1&amp;nbsp;a) State the parent function. [1T]&amp;nbsp;b) Write the function in proper transformation form. [1T]&amp;nbsp;c) Describe the transformations for all parameters, a, k , d and c. [4T]&amp;nbsp;d) Create a transformation table/image table for the function and graph the function. [4A]&amp;nbsp;d) The value for the y – intercept (use algebraic method). [1A]&amp;nbsp;e) The value for the first 2 x – intercept(s) (use algebraic method) between 0°≤𝑥 ≤360° [2T]&amp;nbsp;&amp;nbsp;

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a) State the parent function. [1T]The parent function of the given function is the cosine function, denoted by f(x)=cos(x).b) Write the function in proper transformation form. [1T]To write the function in proper transformation form, we need to identify and apply the necessary transformations. The general form of a cosine function with transformations is given by:f(x)=a·cos(k(x−d))+cIn this case, the given function is g(x)=−2cos(2x+180)−1. We can rewrite it in the proper transformation form as:g(x)=−2cos(2(x+1802))−1c) Describe the transformations for all parameters, a, k, d, and c. [4T]- Amplitude (a): The amplitude of the cosine function determines the vertical stretch or compression. In this case, a=−2, which means the graph is reflected across the x-axis and vertically stretched by a factor of 2.- Period (T) and Frequency (k): The period of the cosine function is determined by the coefficient of x inside the cosine function. In this case, k=2, which means the graph completes one full cycle in 2π2=π units. Therefore, the period is π units, and the frequency is 1π.- Phase Shift (d): The phase shift of the cosine function determines the horizontal shift of the graph. In this case, d=−1802=−90, which means the graph is shifted to the right by 90 units.- Vertical Shift (c): The vertical shift of the cosine function determines the upward or downward shift of the graph. In this case, c=−1, which means the graph is shifted downward by 1 unit.Therefore, the transformations for all parameters are:- The graph is reflected across the x-axis and vertically stretched by a factor of 2.- The graph completes one full cycle in π units, with a frequency of 1π.- The graph is shifted to the right by 90 units.- The graph is shifted downward by 1 unit.

Consider the function 𝑔(𝑥)=−2cos(2𝑥+180)−1 a) State the parent function.

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