Descrivi come si comporta il grafico della funzione esponenziale \( f(x) = 2^x \).

Graph \( y=f(x) \) and \( y=x \). Then graph \( y=f^{-1}(x) \) \( f(x)=(x+4)^{2}, x \geq-4 \)

box is made from a piece of cardboard that measures 15 by 9 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular hat size square should be cut from each comer to obtain maximum volume? with a side of length \( \square \) inches should be cut away from each corner to obtain the maximum volume. to the nearest hundredth as needed.)

Given the following function, (a) find the vertex; (b) determine whether there is a maximum or a minimum value, and find the value; (c) find the range; and (d) find the intervals on which the function is increasing and the intervals on which the function is decreasing. \( f(x)=3 x^{2}+6 x-45 \) Select the correct choice below and fill in the answer box within your choice. (Type an integer or a fraction.) A. The parabla opens downward and has a maximum value of B. The parabola opens upward and has a minimum value of (c) What is the range of \( f(x) \) ? The range of \( f(x) \) is \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) (d) On what interval is the function increasing? The function is increasing on \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

d) \( f(x)=\sqrt{x}-x+2, A(1 \mid f(1)) \)

Restrict the domain of \( f(x) \) so that \( f \) is one-to-one. Then find \( f^{-1}(x) \). \( f(x)=1-x^{2} \)