Calculus Test 1

  1. Specify the domain of the function y = |x – 1|.

  2. Which of the following is a true statement about the graph of the equation y = x^4 +1?
  3. 1. It is symmetric about the x-axis.
    2. It is symmetric about the y-axis.
    3. It has two x-intercepts.
    4. It has no x-intercepts.

    a. Only statements 2 and 3 are true.
    b. Only statements 2 and 4 are true.
    c. Only statements 1 and 3 are true.
    d. Only statement 2 is true.


  4. Which of the following statements are true of the graph of y = \frac{2x-1}{x+1} ?

    1. It has no x-intercept.
    2. It has a slant asymptote y=2x.
    3. It has a vertical asymptote at x=-1.
    4. It has a horizontal asymptote at y=2.

    a. Statements 1, 2, and 3 are true.
    b. Statements 3 and 4 are true.
    c. Statements 2, 3, and 4 are true.
    d. All four statements are true.


  5. Let f(x) = 2 \cos x. The domain of f^{-1}(x) is

    1. [-1,1] 2. (2,  \infty) 3. (-\infty,  \infty) 4. (-2,2) 5. [-2,2]


  6. Simplify as far as possible. \ln e +a^{\log_{a}5}- \log100+10^0 - \log_{3} \frac{1}{3}
  7. Solve for x.

    a. \log_3 x + \log_3(2x+5)=1

    b. \frac{1}{\sqrt{2}}=4^{x}


  8. f(x)=(x-3)(x+1)^2(x-1)^4
  9. Identify the parts of the following composite function. f(g(h(j(x))))=\frac{1}{\sqrt{\log(x-1)}}
  10. Consider the picture below. Find the equation of the line L.


  11. The following table represents a function of the form f(x)=ab^{x}. Find the equation of the function.

     \begin{tabular}{| l | c | r |}  \hline  x & f(x)\\ \hline    0 & 6\\ \hline    1 & 18\\ \hline    2 & 54\\ \hline    3 & 162\\ \hline    4 & 486\\  \hline  \end{tabular}
  12. Given a^{m}=2, a^{n}=3, b^{m}=4, and b^{n}=5,
    use the properties of exponentials to determine (a^{3n}b^{m+n})^{\frac{1}{3}}.


  13. Evaluate:
    1. \sin \frac{\pi}{3}
    2. \tan \frac{3\pi}{4}
    3. \cos \frac{5\pi}{6}
  14. Find all solutions to the equaion, \tan^{2}x=\tan x, such that x \in [0,2\pi].
    Express the answers in radians.


  15. Find f^{-1}(x) if f(x) =  \sqrt{e^{x}+2}.
all real numbers
b
b
5
6
1. Set x equal to 0 to find the y-intercept.
2. Set the values in parentheses equal to 0 to get the x-intercepts 3, —1, and 1.
4. Note that the function will not cross the x axis with an even power, but will cross with an odd power.

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