Below is the graph of \( y=e^{x} \) Transform it to make the graph of \( y=e^{x+6}-3 \). Give the domain and range of \( y=e^{x+6}-3 \) using interval notation.

Consider the following function. \[ m(x)=\frac{1}{(x+1)^{2}}+2 \] Step 1 of 2 : Determine the more basic function that has been shifted, reflected, stretched, or compressed. Answer \[ f(x)= \]

11 My computer has a program that can work out the decimal value of \( \pi \) to a large numbers of digits. You can specify the number of digits required. The time it takes is directly proportional to the square of the number of digits specified. The computer can work out \( \pi \) to 5000 significant figures in exactly half a second. a) Find a formula for the number of digits, \( n \), that the computer can work out in \( t \) seconds. b) Use the formula to find out how long it would take to calculate \( \pi \) to one million digits. c) How many digits can the computer work out in 10 minutes?

2. Esboce o gráfico da função \( f:[0,3] \longrightarrow[-2,10] \) dada por \( f(x)=x^{2}+x-2 \). Verifique se \( f \) é invertível. Se o for, determine sua inversa \( f^{-1} \). 3. Mostre que dentre todos os retângulos de mesmo perímetro o de maior área é o qua- drado.

2. Esboce o gráfico da função \( f:[0,3] \longrightarrow[-2,10] \) dada por \( f(x)=x^{2}+x-2 \). Verifique se \( f \) é invertível. Se o for, determine sua inversa \( f^{-1} \). 3. Mostre que dentre todos os retângulos de mesmo perímetro o de maior área é o qua- drado.

Consider the following piecewise-defined function. \[ f(x)=\left\{\begin{array}{ll}\frac{-5}{x+3} & \text { if } x<-3 \\ -9 & \text { if } x=-3 \\ -x^{2}+4 & \text { if } x>-3\end{array}\right. \] Step 2 of 3 : Evaluate this function at \( x=-3 \). Write the exact answer. Do not round. If the answer is undefined, write Und as your answer. Answer \( f(-3)= \)