008A Sample Final A

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Question 1  Find ${\displaystyle f^{-1}(x)}$ for ${\displaystyle f(x)=\log _{3}(x+3)-1}$

Question 2  Find f(5) for f(x) given in problem 1.

Question 3  a) Find the vertex, standard graphing form, and X-intercept for ${\displaystyle x=-3y^{2}-6y+2}$

b) Sketch the graph. Provide the focus and directrix.

Question 4  Solve. Provide your solution in interval notation. ${\displaystyle (x-4)(2x+1)(x-1)<0}$

Question 5  Graph the system of inequalities ${\displaystyle y<\vert x\vert +1}$           ${\displaystyle x^{2}+y^{2}\leq 9}$

Question 6  Sketch ${\displaystyle 4x^{2}+9(y+1)^{2}=36}$. Give coordinates of each of the 4 vertices of the graph.

Question 7  Solve ${\displaystyle 2\vert 3x-4\vert -7=7}$

Question 8  Given a sequence ${\displaystyle 27,23,19,15,\ldots }$ use formulae to compute ${\displaystyle S_{10}}$ and ${\displaystyle A_{15}}$.

Question 9  a) List all the possible rational zeros of the function ${\displaystyle f(x)=x^{4}+5x^{3}-27x^{2}+31x-10}$
b) Find all the zeros, that is, solve f(x) = 0

Question 10  Graph the function. Give equations of any asymptotes, and list any intercepts ${\displaystyle y={\frac {x-1}{2x+2}}}$

Question 11  Decompose into separate partial fractions ${\displaystyle {\frac {3x^{2}+6x+7}{(x+3)^{2}(x-1)}}}$

Question 12  Find and simplify the difference quotient ${\displaystyle {\frac {f(x+h)-f(x)}{h}}}$ for f(x) = ${\displaystyle {\frac {2}{3x+1}}}$

Question 13  Set up, but do not solve, the following word problem.
One evening 1500 concert tickets were sold for the Riverside Jazz Festival. Tickets cost $25 for a covered pavilion seat and$15 for a lawn seat. Total receipts were \$28,500. How many of each type of ticket were sold?

Question 14  Compute ${\displaystyle \displaystyle {\sum _{n=1}^{\infty }5\left({\frac {3}{5}}\right)^{n}}}$

Question 15  a) Find the equation of the line passing through (3, -2) and (5, 6).
b) Find the slope of any line perpendicular to your answer from a)

Question 16  Solve. ${\displaystyle \log _{6}(x+2)+\log _{6}(x-3)=1}$

Question 17  Compute the following trig ratios: a) ${\displaystyle \sec {\frac {3\pi }{4}}}$       b) ${\displaystyle \tan {\frac {11\pi }{6}}}$       c) ${\displaystyle \sin(-120)}$

Question 18  Compute ${\displaystyle \cos(\arctan {\frac {5}{3}})}$

Question 19  Compute ${\displaystyle \arcsin -{\frac {\sqrt {3}}{2}}}$. Provide your answer in radians.