December 22, 2016
Precalc Warm Up # 1-4
Solve the following equations. Give exact answers if possible. Do
not use logarithms:
x
1. 8 + 3 = 7
1
___
x
2. 4 = 32
x
3. 2 = 20
4. State if the following show exponential growth or decay.
a. f(x) = 3(.8)x
b. f(x) = .4(5)x
c. f(x) = ex
d. f(x) = 3-x
e. sketch f(x) = 2x
f. sketch f(x) = 2x-4 + 3
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2.
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3.
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4.
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December 22, 2016
Investigation of inverse functions.
a. Fill in the table for y = 2x
b. Fill in the table for the
inverse of y = 2x
c. Graph both of these table on the same set of axes. Write
a paragraph about what you notice.
December 22, 2016
Algebra: Switch x and y and solve for y to find the inverse.
f(x) = 2x
let y = f(x)
y = 2x
switch x and y
x = 2y
switch x and y
log2x = ylog22
y = log2x
since log22 = 1
so f -1(x) = log2x
December 22, 2016
As we found in the investigation the inverse of an exponential
function is the reflection across the line y=x.
December 22, 2016
What we know about a logarithmic function f(x) = logax:
• the domain is the set of positive real numbers
• the range is the set of all real numbers
• the curve does not intercept the y-axis
• the y-axis is a vertical asymptote
• the x-intercept is 1
• the graph is continuously increasing
December 22, 2016
Transformation of the logarithmic function
We can use the methods that we already know to
transform the graphs of logarithmic functions.
December 22, 2016
Graph y = log3x and y = log3(x+2)-1 on the
same graph.
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Natural Logs
ln x = log e x
Use a calculator to evaluate natural logs
ln 4
=
ln 2
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The inverse of y = ln x is y = ex
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RECAP:
1. loga(ax) = x and alogax = x
2. ln(ex) = x and elnx = x
3. log(10x) = x and (10logx) = x
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