Question

# This part of the question concerns the graph of the function f(x)=(x+3)^{2}-1 (i) Explain how the graph of f can be obtained from the graph ofy = x² by using appropriate translations. (ii) Write down the image set of the function f, in interval notation. (b) This part of the question concerns the function g(x)=(x+3)^{2}-1 \quad(-3 \leq x \leq 0) The function g has the same rule as the function f in part (a), but a smaller domain. (i) Sketch the graph of g, using equal scales on the axes. (You should draw this by hand, rather than using any software.) Mark the coordinates of the endpoints of the graph. (ii) Give the image set of g, in interval notation. (iii) Show that the inverse function g`has the rule g^{-1}(x)=-3+\sqrt{x+1} justifying each step clearly, and give its domain and image set. (iv) Add a sketch of y = g−¹(x) to the graph that you produced inpart (b)(i). Mark the coordinates of the endpoints of the graph ofg¯¹(x).  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9  Fig: 10  Fig: 11  Fig: 12  Fig: 13