A rancher plans to use 800 feet of fencing and a side of his barn to form a rectangular boundary for cattle. What dimensions of the rectangle would give the maximum area? What is that area?

Step 2 of 2 : Determine the domain and range of the original function. Express your answer in 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 \[ f(x)= \]

\( y = \frac { \sqrt { 2 x - 1 } } { 3 x ^ { 2 } - 1 } \quad [ \frac { 1 } { 2 } \leq x \)

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 \( f(-3)= \)

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.