1. Have out:
Assignment, pencil, red pen, highlighter, GP notebook, graphing calculator
U3D3
Bellwork:
Solve each of the following for x. 1) 2) 3) 4) +1 +2 +2 +1 +2 +2
total:

2. Solve Exponential Equations
Add to your notes:
Solve Exponential Equations
Steps:
Example #1:
1. Rewrite each base to make a common base. (Refer to your powers worksheet.)
2. By the property of equality, if the bases are equal, then the exponents are equal.
3. Set the exponents equal and solve for x.

3. Solve Exponential Equations
Add to your notes:
Solve Exponential Equations
Steps:
Example #2:
1. Rewrite each base to make a common base. (Refer to your powers worksheet.)
2. By the property of equality, if the bases are equal, then the exponents are equal.
3. Set the exponents equal and solve for x.

4. Solve Exponential Equations
Add to your notes:
Solve Exponential Equations
Steps:
Example #3:
1. Rewrite each base to make a common base. (Refer to your powers worksheet.)
2. By the property of equality, if the bases are equal, then the exponents are equal.
3. Set the exponents equal and solve for x.

5. Investigating Asymptotes
Take out the
worksheet:
Investigating Asymptotes
Determine the following information for the function below, and then graph it.
Enter the equation into your graphing calculator in Y=
Type into your graphing calculator: ___________.
1) y-intercept: _______

6. Fill in the values for each table on parts (2), (3), and (5).
Recall the steps for getting single values:
2nd
QUIT
VARS 
Y–VARS
1: Function
1: Y1 ( )
Fill in the x–values here
Use
2nd
ENTER
to repeat the steps.
2) What happens as x gets small?
3) What happens as x approaches 3?
From the left
From the right x y1 x y1 x y1
–0.33 1
–0.5 5
0.5 –1
–0.25 2 –1 4 1 –2
–0.20
2.5 –2
3.5 2
–10
–0.08
2.9
–10
3.1 10
–100
–0.0097
2.99
–100
3.01
100
–1000 –
2.999
–1000
3.001
1000
y approaches 0.
y is more negative.
y gets larger.

7. 5) What happens as x gets large?y x 10
–10
x = 3
5) What happens as x gets large? x y1
vertical asymptote 6
0.33 10
0.14
100
0.01
1000
0.001
y gets closer to zero.
Plot the points from the tables in parts (2), (3), and (5).
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4) When x = 3, the function is _________, so x  3. At x = 3, there is a “invisible” vertical barrier called an __________.
asymptote

8. zero
6) As x gets large or small, y1 approaches _____, but never reaches _____, so we have a __________________ at y = ___.
zero
horizontal asymptote
x = 3 y x 10
–10 7)
Domain: ___________
vertical asymptote
Range: ____________
horizontal asymptote
y = 0

9. Investigate the given function. Be sure to label each graph.
Example #2: Reciprocal function
a) Algebraically solve for the y–intercept.
b) Algebraically solve for the x–intercepts.
This doesn’t make sense.
0 times anything is 0, so 0(x + 3) = 0, not –1.
There is no solution.
cross multiply
Therefore, there are no x–intercepts.

10. Example #2: Reciprocal function
Type f(x) into your calculator, then use to help you graph the function.
TABLE y x 10
–10
x = –3
c) Since x  ___, there is a ______________ at x = __. –3
vertical asymptote –3
d) Is there a horizontal asymptote?
y = 0
As x  , y  ___
As x  – , y  ___
Therefore, y = ___ is a _________ asymptote.
horizontal

11. Investigate the given function. Be sure to label each graph.
Example #3: Reciprocal function
a) Algebraically solve for the y–intercept.
b) Algebraically solve for the x–intercepts.
cross multiply

12. Example #3: Reciprocal function
Type the f(x) into your calculator, then use to help you graph the function.
TABLE y x 10
–10
x = –4
c) Since x  ___, there is a ______________ at x = __. –4
vertical asymptote –4
d) Is there a horizontal asymptote?
As x  , y  ___
As x  – , y  ___ –2
y = –2 –2
Therefore, y = ___ is a _________ asymptote. –2
horizontal

13. Complete the worksheet
Today’s assignment:
Complete the worksheet