Final Exam

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Question

Final Exam

1. Solve the equation

\frac{x + 1}{2 x - 1} + 1 = \frac{4}{x}

2. Solve the equation

\sqrt{1 - 2 x} = \sqrt{x} + 1

3. Find the slope and equation of the line that contains (2,-1) and (3,-3)

4. Graph the parabola

y = - x^{2} + 6 x + 16 . F i n d i t s v e r t e x, l a b e l t h e x a n d y i n t e r c e p t s, i f t h e y e x i s t

5. Constuct the sign chants of

f (x) = (x - x^{2}) {(x + 2)}^{2} a n d s k e t c h i t s g r a p h

6. Construct the sign chants and sketch the graph of

y = \frac{2 x - 1}{x + 3}

. Label the x&y intercepts and asymptotes

7. Given the equation of a circle

x^{2} - 8 x + y^{2} + 4 y = - 4 . C o m p l e t e t h e s q u a r e t o f i n d i t s r a d i u s a n d c e n t e r . G r a p h i t a n d l a b e l t h e f o u r c a r d i n a l p o i n t s .

Simplify

\frac{f (x + h) - f (x)}{h}, m a k e s u r e t h e h i s c a n c e l l e d

f (x) = - 2 x^{2} - 3 x

f (x) = 2 / (1 - 3 x),

Solve the following equations without the calculator

10.

\log_{x} (\frac{x + 3}{2}) = 2

11.

\frac{e^{x^{2}}}{e^{2}} = e^{x}

Solve. Give te exact answer and the approximate answer to three significant digits using the calculator

12.

4 + 3 * e^{2 x + 1} = 6

13.

5 L n (3 - 7 x) - 9 = 23

14. Combine into a single log:

1 / 2 * L O G (x - 2) - L O G (x + 1) - L O G (x - 1)

15. Solve without the calculator :

\log_{8} (x + 1) + \log_{8} (x - 1) = 1

16. Compute the sum

\sum_{n = 3}^{6} {(- 1)}^{n} (1 - 2 n^{2})

17. Find the inverse matrix

A^{- 1} o f

. Check that

A^{- 1} A = 1

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This question is taken from Math 260 – PreCalculus » Summer 2021 » Exams