Mercer County Community College    MAT146      PRECALC     Prof. Porter's   Practice Midterm

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Formulas:

P=Qe^RT

P=Q(1+R/N)^NT

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1. Use the following data to answer the questions below.

=            =

-2	0.1
-1	0.9
0	2.2
1	3.1
2	4.0
a.) Plot the data points on the graph										2
										1
b.) Draw a line of best fit on the								-2	-1	0	1	2
Graph above: that is, draw a										-1
Straight line which comes as close										-2
As possible to all the data points
(this is also called the regression
Line).
c.) Use the calculator to give the equation of the regression

                                                                                                                Regression:_______________________

2. Find the Vertical and Horizontal Asymptotes for:

                                                Vertical:

Horizontal:

                                                Vertical:

Horizontal:

3. Given the equation:

Find the asymptotes:

                                                Vertical:

Horizontal:

Find the intercepts.

                                                x-intercepts:

                                                y-intercepts:

Give a qualitative graph for the entire function. Show the asymptotes and intercepts.

 

4. Sketch the graph of .

State the Domain _______________         State the Range ________________

State the asymptote _____________         State the y-intercept _____________

5. Find the inverse for the function.

                                                                                                                                ANSWER:____________________

Use the inverse to help find the x-intercept in the problem .

Give your answer to TWO DECIMAL PLACES

                                                                                                                                ANSWER:____________________

6. Consider the  function: g(x) =  log (x + 3) + 4

State the Domain _______________         State the Range ________________

State the asymptote _____________         State the y-intercept _____________

State the x-intercept _____________

7. In 1950 the radiation levels were fount to be 1400 bars. In 1970 the levels had dropped to 700 bars. Assuming the decay is exponential in nature

Determine the rate of decay “r”

Rate:____________

What is the half life (in years)?

                                                                                    Half-life:_________

What do you estimate the level of radiation to be in 2000?

8. Suppose bank A is offering 5.1% on a CD that compounds monthly, but bank B is offering 5.05% on a CD compounding continuously.

How much money would I have if I invested $1000 in each account for two years?

                                                                                                                                Bank A:____________________

                                                                                                                                Bank B:____________________

How could I earn the most on my $2000 ?

                                                                                                                                ANSWER:____________________

9. Solve the following:

                                                                                                                                ANSWER:____________________

Suppose log₃2 = .6, without a calculator how could you find log₃(18) or log₃(2 x 3²)?

                                                                                                                                ANSWER:____________________

10. Solve the following for x (exactly):

                                                                                                                                ANSWER:____________________

                                                                                                                                ANSWER:____________________

11. If it is possible for Don to sell 300 bells at $10 a piece or 50 bells at $30 a piece, use a linear relationship to describe the number of bells N he can sell given the price P? 

(leave the equation in point -slope or slope intercept form)

                                                                                Answer:_________________________

12. Given the function f(x) = 2 +  3x²

Find and simplify:

                                                                                Answer:_________________________

13. An open box is created by cutting squares with sides of length x from the corners of a piece of cardboard with dimensions 400 by 30.

If the volume is given by the equation V = x (400 - 2x) ( 30 - 2x)

Give a qualitative graph of the function:

What is the degree of the polynomial function?______________

How many faces could any polynomial of that degree have?_______________________________

Can there be only one complex root? Why?___________________________________________

14. Given the functions below, 

Find (f o g)(1).

                                                                                (f o g)(1)_________________________

What is the domain for (f + g ) (x) ?

                                                                                Domain:___________________

15. Given the functions below, 

Find  g^-1(x)

                                                                                g^-1(x) = _________________________

Find  (g o g^-1)(10¹⁰⁰)

                                                                                 (g o g^-1)( 10¹⁰⁰)._________________________