How are the functions \( y=x \) and \( y=x-1 \) related? How are their graphs related? Each output for \( y=x-1 \) is 1 more than the corresponding output for \( y=x \). The graph of \( y=x-1 \) is the graph of \( y=x \) translated down 1 unit. Each output for \( y=x-1 \) is 1 less than the corresponding output for \( y=x \). The graph of \( y=x-1 \) is the graph of \( y=x \) translated up 1 unit. Each output for \( y=x-1 \) is 1 more than the corresponding output for \( y=x \). The graph of \( y=x-1 \) is the graph of \( y=x \) translated up 1 unit. The graphof \( y=x-1 \) is thegraphaf \( y-x \) t tuaplates doun 1 urit. Each output for \( y=x-1 \) is 1 less than the corresponding output for \( y=x \). The graph of \( y=x-1 \) is the graph of \( y=x \) translated down 1 unit.

Perform the following arithmetic operations on the given complex numbers. a. Add. \( (1+5 i)+(-1+2 i) \) b. Subtract. \( (1+5 i)-(-1+2 i) \) c. Multiply. \( (1+5 i)(-1+2 i) \) d. Divide. \( \frac{1+5 i}{-1+2 i} \) e. Evaluate. \( i^{71} \). ( \( 1+5 \).

18. निम्न में कौन से घुल समताथ भिन्त है- \( \begin{array}{lll}\text { (a) } \frac{-13}{9} \cdot \frac{39}{-27} & \text { (b) } \frac{3}{-7} \cdot \frac{-18}{42} & \text { (c) } \frac{15}{14}, \frac{-225}{-210} \\ \text { (d) } \frac{-2}{3}=\frac{3}{2} & \text { (e) } \frac{3}{11} \cdot \frac{-3}{11} & \text { (f) } \frac{7}{-19}, \frac{-28}{76}\end{array} \)

Find the length of a rectangle whose area and breadth are respectively: \( (15-18) \) 15. \( (1+a+b+a b) \mathrm{sq} \) unit, \( (a+1) \mathrm{unit} \) 16. \( 184 \mathrm{sq} \mathrm{m} 50 \mathrm{sq} \mathrm{dm}, 12 \mathrm{~m} 3 \mathrm{dm} \). 17. \( 85 \mathrm{sq} \mathrm{m} 86 \mathrm{sq} \mathrm{dm}, 8 \mathrm{~m} .1 \mathrm{dm} \). 18. \( 49 \mathrm{sq} \mathrm{m} .93 \mathrm{sq} \mathrm{dm} 80 \mathrm{sq} \mathrm{cm}, 6 \mathrm{~m} 15 \mathrm{~cm} \).

What are the domain and range of the function defined by \( y=|x+3|-2 \) notation and interval notation? \( \begin{array}{ll}\text { a } \\ \text { domain: }\{x \mid x \geq-3\} ;[-3, \infty) \\ \text { range: }\{y \mid y \geq 0\} ;[0, \infty) \\ \text { domain: }\{x \mid x \geq-3\} ;[-3, \infty) \\ & \text { range: }\{y \mid y \geq 2\} ;[2, \infty) \\ \text { o domain: }\{x \mid x \text { is a real number }\} ;(-\infty, \infty) \\ & \text { range: }\{y \mid y \text { is a real number }\} ;(-\infty, \infty) \\ \text { d domain: }\{x \mid x \text { is a real numbert }\} ;(-\infty, \infty)\end{array} \) range: \( \{y \mid y \geq-2\} ;[-2, \infty) \)

3. The diagram shows a hula hoop with diameter 96.52 cm . Nely spins the hoop for 4 complete rotations. Calculate the distance travelled by the hoop, in metres.