# Precalculus

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1. Which of the following functions would f(x) = log(base 10)x horizontally 4 units to the left?

a) f(x)=log(base10)(x-4)
b) f(x)=4Log(base10)X
c) f(x)=log(base10) x+4

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2. State the transformations, in proper order, that are needed to turn f(x) = -8log(base10)x+6 into f(x)=4log(base10)x+1

a) reflection about the x-axis, vertical compression by a factor of 1/2, vertical translation 5 units down.

b) reflection about the y-axis, vertical stretch by a factor of 2, vertical translation 5 units up.

c) vertical translation 5 units down, vertical compression by a factor of 1/2, reflection about the x-axis.

d) Reflection about the x-axis, vertical translation 5 units down, vertical compression by a factor of 1/2.

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3. Which of the values in general logarithmic function f(x)=alog(base10)(k(x-d)) + c should be multiplied by -1 in order to cause a reflection in the y-axis?

a) a
b) k
c) d
d) c

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4. Which of the following functions results if f(x) log(base 10)x is vertically stretched by a factor of 4, horizontally stretched by a factor of 3, reflected in the y-axis, horizontally translated 5 units to the right and vertically translated 2 units up?

a) f(x)= -4log(base10) [1/3(x-5)] + 2

b) f(x)= 4log(base10) [-1/3(x-5)] + 2

c) f(x)= 4log(base10) [-3(x-5)] + 2

d)f(x)= -4log(base10) [-1/3(x-5)] + 2

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5. Which is the first transformation that should be applied the graph of f(x) = log(base10)x to the graph f(x)=4log(base10)(x-5) + 3?

a) vertical stretch by a factor of 4
b) horizontal translation 5 units to the right
c) vertical translation 3 units up
d)vertical compression by a factor of 4

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6. A certain radioactive isotope has a half life of 5 years. If a sample has 120 grams of radioactive material, what equation could be used to determine the amount of material remaining (y) after x years.

a) y=120 x (1/2)^5x

b) y=60^5x

c) y=120x5^(1/2)^x

d) y=1/2x120^5x

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7. State the law of logarithms used to rewrite log(base 5)32 - log(base 5)8 as log(base 5)4.

a) difference of law of log
b) product law of log
c) power law
d) quotient law

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8. Which of the following log equations is undefined?

a) log(base -x)10=100
b) log(base x) - 10=100
c) log(base10)100=-x
d) log(base10)100=10^-x