Graph the parabola \( g(x) 2(x-1)^{2}-3 \)

FMU Question 1 Use exponent rules to simplify the following, giving all answers with positive exponents. (a) \( 6^{3} \times 6^{-5} \times 6^{-2} \) \( 3+(5)+(-2)=3-5-2=3-7=\frac{1}{64}=6^{-4} \times 6^{-2}=\frac{1}{6} \) \( 6^{3} \times 6^{-5} \times 6^{-2}= \) (b) \( \quad-5\left(a^{3}\right)^{0}-3+4^{0} \)

The infant is born during a. the first stage of labor b. the second stage of labor c. transition d. the third stage of labor

Find the inverse for each of the following functions. \( s(x)=3 x+3 \) \( s^{-1}(x)=\square \) \( r(x)=\sqrt[3]{8 x+5} \) \( r^{-1}(x)=\square \) \( h(x)=9 x^{3}+4 \) \( h^{-1}(x)=\square \) \( k(x)=\frac{5}{x+10} \) \( k^{-1}(x)=\square \)

12. A landscape supply business charges \( \$ 35 \) to deliver mulch. The cost of the mulch is \( \$ 29 \) per cubic yard. Write and solve a linear equation to find the cost of having 6 cubic yards of mulch delivered to a site.

(c) Evaluate the following definite integrals: (i) \( \int_{4}^{5}\left(\frac{2}{\sqrt{x}}-x\right) d x \) (ii) \( \int_{0}^{1} \frac{x}{\left(2 x^{2}+1\right)^{3}} d x \)