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Probability, Equations and Graphs

1. A mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be an S, U or N. Each number must be a 3 or 5. Repetition of digits is permitted.

a. Use the counting principle to determine the number of points in the sample space.
b. Construct a tree diagram to represent this equation.
c. List the sample space.
d. Determine the exact probability of creating a mini license plate with a 3. Give solution exactly in reduced fraction form.

2. Evaluate the exponential equation for three values of x greater than -4, three values of x smaller than -4, and at x = -4. Show your work. Use the resulting ordered pairs to plot a graph. State whether the equation of the line is asymptotic to the graph (if any).

y = 3^(x+4)

3. Evaluate the logarithmic equation for three values of x that are less than -1, three values of x that are between 0 and -1, and at x = -1. Show your work. Use the resulting ordered pairs to plot a graph. State whether the equation of the line is asymptotic to the graph (if any).

y = -log (-x)
3.5

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The solution is comprised of detailed step-by-step calculation and explanation of the given problems. This solution also provides students with a clear perspective of the underlying mathematical aspects.

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