Solve the problems. (1) The length of a rectangle is \( y \) times its width. The width of the rectangle is \( 4 y^{2} \). a. What is the area of the rectangle? b. If \( y \) is 4 , what is the area?

Bxercicio 1 Verifique se as funções abaixo saio transformaçôes lineares: a) \( F: \mathbb{R} \rightarrow \mathbb{R}^{2} \) dada por \( F(x)=(x, 2) \). b) \( F: M_{n \times n} \rightarrow M_{n \times n} \) dada por \( F(X)=P^{-1} X P \), onde \( P_{2 \times 2} \) é uma matriz invertivel fixada. c) \( F: \mathbb{R}^{4} \rightarrow \mathbb{R}^{4} \) dada por \( F(x, y, z, t)=(\cos (x), y, z, t) \). d) \( F: M_{n \times n} \rightarrow M_{n \times n} \) dada por \( F(X)=X A-A X \), onde \( A_{2 \times 2} \) é uma matriz fixada.

Si \( f \) es una función tal que \( D_{f}=[a, b] \), con \( a

Find the domain and the range of the function. \( f(x)=\left\{\begin{array}{ll}-\frac{2}{7} x+5, & \text { for } x<7 \\ 3, & \text { for } x \geq 7\end{array}\right. \)

For the piecewise function, find the values \( g(-7), g(2) \), and \( g(8) \). \( g(x)=\left\{\begin{array}{l}x+8, \text { for } x \leq 2 \\ 4-x, \text { for } x>2\end{array}\right. \)

5. What are three things should you consider when deciding on a career? what your best friend is choosing, what your parents want you to do, and, of course, pay what your parents want you to do, education, and which is the easiest which is the easiest, how much money you will make, and education education required, your passion, and schedule