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29 Cards in this Set
- Front
- Back
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a^m × a^n=…
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a^(m+n)
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a^m / a^n=…
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a^(m-n)
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(a^m)^n=…
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a^(m×n)
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a^n × b^n=…
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(ab)^n
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a^m / b^m=…
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(a/b)^m
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a^(m/n)=…
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(a^(1/n))^m
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What is the general form of a simple exponential function?
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f(x)=a^x
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For very large positive values of x, what value does y approach?
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Infinity
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For very large negative values of x, what value does y approach?
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Zero
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Name of the line that a function gets increasingly close to but never reaches?
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Asymptote
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For all the graphs y=a^x what is the asymptote?
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The asymptote is the x-axis
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For all the graphs y=a^x what is the y-intercept?
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The y-intercept is always (0,1)
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When the base is greater than 1 the function…
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Increases
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When the base is between the values 0 and 1 the function…
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Decreases
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What is the value of 'e'?
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e =2.718….
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For y=10^x how can you express the value of x?
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x=log y
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What is the base of log?
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The base is 10
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What is the base of ln?
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e
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log base a of a^x=…
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x
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a^(log base a of x)=…
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x
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What is the logarithm of a negative number?
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It has no real values
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What is the logarithm of zero?
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It has no real value
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The logarithm of a product (log base a of xy) is…
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the sum of the logarithms( log base a of x + log base a of y)
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The logarithm of a quotient (log base a of x/y) is…
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the difference of logarithms ( og base a of x-y)
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The logarithm of a reciprocal (log base a of 1/x) is…
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the negative of the logarithm (-log base a of x)
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The logarithm of a exponential (log base a ox x^p) is…
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the multiple of the logarithm (p log base a of x)
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What is the logarithm of 1?
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zero
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What is the change of base rule?
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log base b of a= (log base c of a)/(log base c of b)
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For y=log base a of x where does the graph lie?
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To the right of the y-axis
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