Algebraic Structures

Here you will find practice problems aligned with the Cambridge IB SL Chapter 3 textbook. Visit this page directly at hunkim.com/cambridge3

1. Using a graphing calculator, find the point(s) of intersection between f(x)=\ln x^2 and g(x)=6.
2. Using a graphing calculator, find the minimum value of y=-x^2e^{-x} for x\in[0,4].
3. Solve
   1. 2(x+3)^3=0
   2. (\ln x-1)(3x+1)e^x=0
   3. x^4-6=x^2
4. f(x)=\frac{x^3-100x}{x^2-4}
   1. Find the zeros.
   2. Equations of the vertical asymptotes?
5. y=xe^{-x}-3. Does this graph have a horizontal asymptote? If so, what is the line equation?
6. Sketch y=\log |x+3|. Label the x-intercepts.
7. Simplify e^{3\ln x+\ln5}.
8. Solve:
   1. e^x \ln x=5e^x
   2. x\ln x+4\ln x=0
   3. \ln x^2=2
   4. 15^x-25\times 3^x=0
9. Sketch y=e^{-x}+3.
10. How many solutions? e^x=9-x^2

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