Test 3 Sp 21 - adfdf PDF

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MAT 171: TEST 3 SHOW ALL WORK NECESSARY TO SUPPORT YOUR ANSWERS! 1.

y = ( x + 2 )( x −1)

2

( x − 3)

a) Name the x-intercepts, or write none. _____________________

b) Name the y-intercept, or write none. _____________

c) Make an ABOVE/BELOW line. Then stop! Do not graph!

2.

For some graph of a polynomial function, you found the following information: x-intercepts: −4, − 1, 5 y-intercept: 7 ABOVE/BELOW line:

Use all the information above to graph the function. y

x

3.

y=

2x − 6 x+1

a) Find the equation of the horizontal asymptote, or write none. ___________

b) Find the equation of each vertical asymptote, or write none. ___________________

c) Find the y-intercept, or write none. ______________

d) Find each x-intercept, or write none. _____________

e) Make an ABOVE/BELOW line. Remember: Put your numbers from parts (b) and (d) on the number line.

Stop! Do not graph!

4.

For some graph of a rational function, you found the following information: Vertical asymptote: x = 4 Horizontal asymptote: y = 1 The graph does not cross the horizontal asymptote. y-intercept: −5 x-intercept: −2 ABOVE/BELOW line:

Use all the information above to graph the function.

y

x

5.

(

)

Use long division to divide 9 x 2 −12 x − 1  (3 x + 2 ) . Write the answer in this form: Quotient +

6.

(

Remainder . 3x + 2

)

4 2 Use synthetic division to divide 3 x − 2 x − 5 x + 4  ( x − 2 ) .

Write the answer in this form: Quotient +

Remainder . x−2

7.

If −3 is one zero of f ( x ) = x 3 − x 2 − 13 x − 3 : a) Find all the other zeros of the function. Simplify each answer in exact form.

The zeros are ______________________________________________________ b) Express f ( x ) as the product of linear factors.

8.

Find a polynomial f ( x ) of degree 3 with the following zeros: 2 i , − 2 i, 3 . Write your answer in the form ax 3 + bx2 + cx + d .

For #9 and #10: a) Make a POS/NEG number line. b) Graph the solution set on the number line. c) Write the answer in interval notation. 9.

10.

( x − 1 )2 ( x + 3 ) ( x − 5 )  0

2x + 8 0 x− 3

11.

Does the graph represent a one-to-one function? (Yes or No) a)

b)

y

x x

y

___________

__________

12.

h ( x ) = 5 x − 3 . Find h− 1 ( x ) . Show your work!!!

13.

State the domain and the range in interval notation. y 





Domain: __________________

 x −

−

−

−









−

−

−

−

Range: ___________________

14.

1  Graph y =   3 

x −1

− 2 using the following steps.

a) What ordered pair is the new origin? _____________________ b) Write the parent equation you get when you remove the “translators.” _________ c) Make a table for the parent equation that shows three important points.

y

x

d) Plot the new origin from part (a). Then, through the new origin draw a new dashed x-axis and y-axis. Then plot the three points in your table and connect them with an appropriate shape.



y

    x −

−

−

−

 − − − − −









15.

r  Compound Interest Formula: A = P 1 +  

nt

n

a) $7000 is invested at 5% interest compounded daily (365 times per year). Find the amount of money in the investment after 40 years. Round to the nearest cent.

b) After 5 years, the total amount in an investment earning 7% interest compounded monthly (12 times per year) was $7422.69. To the nearest dollar, how much money was originally invested....