​The function 𝑓 is defined by 𝑓⁡(𝑥)=𝑎⁢sin⁡(𝑏⁢(𝑥+𝑐)+𝑑), for constants 𝑎, 𝑏, 𝑐, and 𝑑. In the 𝑥⁢𝑦-plane, the points (2,2) and (4,4) represent a minimum value and a maximum value, respectively, on the graph of 𝑓. What are the values of 𝑎 and 𝑑 ?

Consider the functions 𝑔 and ℎ given by 𝑔𝑥=4𝑥 and ℎ𝑥=16𝑥+2. In the 𝑥𝑦-plane, what is the 𝑥-coordinate of the point of intersection of the graphs of 𝑔 and ℎ ?Responses-4negative 4-2negative 200

The complete graph of the function f is shown in the xy - plane. For what value of x is the valueof f(x) at its minimum

The function 𝑓(𝑥,𝑦)=𝑥3−3𝑥−2𝑥𝑦−𝑦2−2𝑦+4 has two critical points. Find and classify them. the left-most stationary point (the one with the lower value of x) is located at x = and y = and is a point. • the right-most stationary point (the one with the higher value of x) is located at x = and y = and is a point

The function 𝑓 is given by 𝑓⁡(𝑥)=2(3⁢𝑥). Which of the following statements describes characteristics of the graph of 𝑓 in the 𝑥⁢𝑦-plane?ResponsesThe graph of 𝑓 is a vertical dilation of 𝑦=2𝑥, and 𝑓⁡(𝑥) is equivalent to 8𝑥.The graph of  f  is a vertical dilation of  y equals 2 to the power of x , and  f open parentheses x close parentheses  is equivalent to  8 to the power of x .The graph of 𝑓 is a vertical dilation of 𝑦=2𝑥, and 𝑓⁡(𝑥) is equivalent to 8·2𝑥.The graph of  f  is a vertical dilation of  y equals 2 to the power of x , and  f open parentheses x close parentheses  is equivalent to  8 times 2 to the power of x .The graph of 𝑓 is a horizontal dilation of 𝑦=2𝑥, and 𝑓⁡(𝑥) is equivalent to 8𝑥.The graph of  f  is a horizontal dilation of  y equals 2 to the power of x , and  f open parentheses x close parentheses  is equivalent to  8 to the power of x .The graph of 𝑓 is a horizontal dilation of 𝑦=2𝑥, and 𝑓⁡(𝑥) is equivalent to 8·2𝑥.

The graph of 𝑥2+2𝑥+𝑦2+2𝑦=4x 2 +2x+y 2 +2y=4 in the 𝑥𝑦xy-plane is a circle centered at (𝑎,𝑎)(a,a). What is the value of 𝑎a?