Download x =3y

Key
Exploring the Graphs of Logarithmic Functions
1)
!
y = log 3 x
x
1/9
1/3
1
3
9
2)
y
!x = 3
2 y = x, x = 2 y
x
1/4
1/2
1
2
4
Key
y
-2
-1
0
1
2
y
-2
-1
0
1
2
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©Let’s Algebra 2014
3)
7 = x, x = 7
y
y
x
1/7
y
-1
1
0
7
1
4) This part was done for student.
5)
!
y = log 5 x
The x- intercept = 1 and
the point (5, 1) is on the line.
Key
6)
The domain is x > 0. The range is all real numbers.
7)
The x-intercept is (1, 0). There is no y-intercept.
8)
The asymptote is x = 0.
Page 2 of 6
©Let’s Algebra 2014
y = log 5 x
9)
y = log 5 (x ! 3) + 2
The x-intercept = 1
The point ( 5 , 1 ) is on the line.
(8, 3)
(4, 2)
The domain of the “new” function is
x>3
The range of the “new” function is
all real numbers.
The asymptote of the “new function
is x = 3
Exercises
a)
!
y = log 8 x The x- intercept = 1 and the point (8, 1) is on the line.
The domain is x > 0.
The range is all real numbers.
The x-intercept is (1, 0)
The y-intercept is…there is no y-intercept.
The asymptote is x = 0.
Key
Page 3 of 6
©Let’s Algebra 2014
b) ! y = log 4 x The x- intercept = 1 and the point (4, 1) is on the line.
The domain is x > 0.
The range is all real numbers.
The x-intercept is (1,0)
The y-intercept is …there is no y-intercept.
The asymptote is x = 0.
c)
! y = log x The x- intercept = 1 and the point (10, 1) is on the line.
The domain is x > 0.
The range is is all real numbers.
The x-intercept is (1,0)
The y-intercept is…there is no y-intercept
The asymptote is x = 0.
Key
Page 4 of 6
©Let’s Algebra 2014
y = log 6 x
d)
y = log 6 (x ! 2) ! 3
The x-intercept is 1.
The point (6, 1) is on the graph.
The domain of the “new”
function is x > 2.
The range of the “new”
function is all real numbers.
(3, –3)
(8, –2)
y = log 8 x
e)
The asymptote of the “new”
function is x = 2.
y = ! log 8 (x + 4) ! 1
The x-intercept is 1.
The point (8, 1) is on the graph.
The domain of the “new”
function is x > -4
The range of the “new” function
is all real numbers.
The asymptote of the “new”
function is x = -4.
(–3, –1)
Key
(4, –2)
Page 5 of 6
©Let’s Algebra 2014
Without graphing, describe the transformation from the parent function.
f)
It is translated right 1 unit.
g)
It is translated down 1 unit.
h)
It is translated right 2 units and down 5 units.
i)
It it vertically compressed by a factor of .5 and reflected across the x-axis, then translated
right 1 unit, and up 2 units.
j)
It is vertically stretched by a factor of 2 and reflected across the x-axis, then translated
left 5 units, up 3 units.
Key
Page 6 of 6
©Let’s Algebra 2014