Given the graph of \( y=f(x) \), if \( c \) is a positive real number, then which of the following statements best describes how to sketch the graph of \( y=f(x)+c \) ? Choose the correct answer. A. The graph of \( y=f(x)+c \) can be obtained by horizontally shifting the graph of \( y=f(x) \) to the left \( c \) units. B. The graph of \( y=f(x)+c \) can be obtained by vertically shifting the graph of \( y=f(x) \) up \( c \) units. C. The graph of \( y=f(x)+c \) can be obtained by vertically shifting the graph of \( y=f(x) \) down \( c \) units. D. The graph of \( y=f(x)+c \) can be obtained by horizontally shifting the graph of \( y=f(x) \) to the right \( c \) units.

\( \left(2 x^{2}-3 x+9\right)(x-5) \) (2) \( \left(x^{2}-2 x+1\right)\left(x^{2}+3 x+4\right) \) (3) \( (x-2 y)\left(2 x^{2}-3 x+4 y^{2}\right) \) (4) \( \left(3 x^{2}-x+2\right)\left(x^{2}-4 x+5\right) \) (3) \( \left(x^{2}+3 x+2\right)\left(x^{2}-x+1\right) \)

4. Resuelva las siguientes operaciones con número racionales. \( \left(-\frac{3}{5}\right)\left(\frac{4}{7}\right)\left(-\frac{1}{6}\right) \) \( \left(-\frac{11}{7}\right)\left(-\frac{5}{9}\right)\left(-\frac{15}{6}\right) \) \( \left(-\frac{2}{5}\right)\left(-\frac{45}{2}\right) \) - \( (-7)\left(-\frac{5}{8}\right)\left(-\frac{9}{7}\right) \) - \( \left(-\frac{4}{5} \div-\frac{3}{4}\right. \) \( \frac{9}{8} \div \frac{7}{5} \)

2. A rectangular prism is 4 inches long, 3 inches wide, and 8 inches tall. Which expression can be used to find the volume of the rectangular prism in cubic inches? (A) \( (4 \times 3) \times 8 \) (B) \( 4+3+8 \) (C) \( (4 \times 3)+8 \) (D) \( 4-(3 \times 8) \)

Dada la matriz A a. Resuelva el sistema \( (A-\lambda I) X=0 \) b. Con los \( X \) obtenidos en (b) arme una matriz \( P \) y encuentre su inver c. Encuentre \( P^{-1} A P \).

A) \( 0,5 \mathrm{~m} \). B) \( 0,9 \mathrm{~m} \). C) 1 m . D) \( 1,8 \mathrm{~m} \). C) 2 m .