# Precalculus questions with polynomials, exponentials, etc.

1.) If f(x) = x^3 + 3x^2 - 1, which of these is true?

I. f has domain all real numbers

II. f is a 1-1 function

III. f is onto the set of real numbers

a. Only one (could be any one

b. I and II

c. II and II

d. I and II

e. All three

2) solve e^x +2x =7

3) If log 3 = 1.4 and log5 = 3.6, find log 45

4) Find the period of f(x)= 3-2cos(3x + π)

5) find csc(arctan 8/15)

6) for x ?[0, 2π), solve: cos2x = cosx

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#### Solution Preview

1.) If f(x) = x^3 + 3x^2 - 1, which of these is true?

I. f has domain all real numbers

This is true because you can substitute any real number in for x and the value of f will still be a real number.

II. f is a 1-1 function

This is not true. The graph of this function does not pass the horizontal line test. If you draw a horizontal line across this function, it will cross more than once when the line is drawn at certain positions.

III. f is onto the set of real numbers

This is true. The range of this function contains all real numbers so this function is onto.

Answers (d) should be the correct answer.

a. Only one (could be any ...

#### Solution Summary

Six precalculus questions involving polynomials, exponential functions, logarithmic functions, and trigonometric functions.