Assignment, pencil, red pen, highlighter,
GP notebook, graphing calculator
Solve each of the following for x.
1)
x
7
4 4
x 7
+2
2)
8
2x
3 3
8  2x
x 4
3)
+1
3
3
x 5
x  5 +2
4)
+2
5
(3x1)
9 9
5  3x 1
6  3x +1
x 2
+2
total:
10
Steps:
Example #1: 4 x  64 x 3
1. Rewrite each base to make
4x  43x3
a common base. (Refer to
x  3x  3
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.
x  3x  9
 3x  3x
 2x  9
9
x
2
Steps:
Example #2: 25 x  625 4x
1. Rewrite each base to make
2(x)
4( 4x)
5
5
a common base. (Refer to
your powers worksheet.)
2(x)  4( 4x)
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.
2x  16x
 2x  2x
0  18x
0
x
 18
x 0
1
x 7
Steps:
Example #3:

81
5x
9
1. Rewrite each base to make
1(5x)
2(x7)
a common base. (Refer to
9
9
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.
 1(5x)  2(x  7)
 5x  2x  14
 2x  2x
 7x  14
x  2
Determine the following information for the function below, and
then graph it.
1
Enter the equation Y1 
into your graphing calculator in Y=
x 3
1  (x  3)
Type into your graphing calculator: ___________.
1

 0,  
3
1) y-intercept: _______
1
1
Y

03 3
Fill in the values for each table on parts (2), (3), and (5).
Recall the steps for getting single values:
VARS

Use 2nd
Y–VARS
ENTER
2) What happens
as x gets small?
x
0
–1
–2
–10
–100
–1000
y1
–0.33
–0.25
–0.20
–0.08
–0.0097
–0.000997
y approaches 0.
1: Function
1: Y1
2nd QUIT
(
)
Fill in the x–values here
to repeat the steps.
3) What happens as x approaches 3?
From the left
From the right
x
1
2
2.5
2.9
2.99
2.999
y1
–0.5
–1
–2
–10
–100
–1000
y is more negative.
x
5
4
3.5
3.1
3.01
3.001
y1
0.5
1
2
10
100
1000
y gets larger.
y
5) What happens as x
gets large?
x
6
10
100
1000
10
y1
0.33
0.14
0.01
0.001
vertical
asymptote
x
–10
y gets closer to zero.
x=3
10
1
Y1 
x 3
Plot the points from the
tables in parts (2), (3),
and (5).
–10
undefined so x  3. At x = 3,
4) When x = 3, the function is _________,
asymptote
there is a “invisible” vertical barrier called an __________.
zero but never
6) As x gets large or small, y1 approaches _____,
zero so we have a __________________
0
horizontal asymptote at y = ___.
reaches _____,
x=3

x|x  3 
7) Domain: ___________
y |y  0 
Range: ____________
y
10
vertical
asymptote
y = 0 horizontal asymptote
–10
x
10
1
Y1 
x 3
–10
Investigate the given function. Be sure to label each graph.
1
Example #2: Reciprocal function f(x) 
x3
a) Algebraically solve for the y–intercept.
1
1
f(0) 

03
3
  1
 0, 
 3 
b) Algebraically solve for the x–intercepts.
1
0
x3
0
1

1 x3
cross multiply
0(x  3)   1
This doesn’t make sense.
0 times anything is 0, so 0(x + 3) = 0, not –1.
There is no solution.
Therefore, there are no x–intercepts.
1
Example #2: Reciprocal function f(x) 
x3
Type f(x) into your calculator, then use TABLE to help you
y
graph the function.
x = –3
–3 there is a
c) Since x  ___,
–3
vertical
asymptote at x = __.
______________
10
d) Is there a horizontal
asymptote?
y=0
0
As x  , y  ___
0
As x  – , y  ___
x
–10
10
0 is a
Therefore, y = ___
horizontal asymptote.
_________
–10
Investigate the given function. Be sure to label each graph.
1
2
Example #3: Reciprocal function f(x) 
x4
a) Algebraically solve for the y–intercept.
1
1
1 8
7
f(0) 
2  2    
04
4
4 4
4
7

 0,  
4

b) Algebraically solve for the x–intercepts.
1
0
2
x4
1
2
x4
cross multiply
2(x  4)  1
2x  8  1
2x   7
7
x
2
 7 
 , 0
 2 
1
2
Example #3: Reciprocal function f(x) 
x4
Type the f(x) into your calculator, then use TABLE to
y
help you graph the function. x = –4
–4 there is a
c) Since x  ___,
vertical
asymptote at x = –4
______________
__.
10
d) Is there a horizontal
asymptote?
–2
As x  , y  ___
–2
As x  – , y  ___
x
–10 y = –2
10
–2 is a
Therefore, y = ___
horizontal asymptote.
_________
–10
Today’s assignment:
Complete the worksheet