Mathematical Scratchpad

Review for test 2 Math 140

  1. Let $f$ be the function graphed below:

    1. Does $f$ have an inverse in the domain of $[-4,4]?$ Explain.

    2. If we restrict the domain of $f$ to be $[-2,2],$ does $f^{-1}$ exist? Explain.

    3. If $f(-2)=-1,$ $f(-1)=-3$ and $f(2)=-7,$ find $f^{-1}(-1),$ $f^{-1}(-3) $ and $f^{-1}(-7).$

  2. Describe how you can find the relationship among three sides of a right triangle when the angles are MATH and $90^{\circ }$ respectively.

  3. Repeat problem above by using MATH and $90^{\circ }$.

  4. For MATH Find (a) $\sin \theta $ (b) $\cos \theta .$

  5. If MATH and MATH Find $(a)\cos (\pi -t),$ $(b)\sin t.$

  6. $f(x)=-\sqrt{3x-2}.$ Find the inverse function for $f$ if it exists. If they exist, graph $y=f(x)$ and $y=f^{-1}(x)$ together.

  7. If the graph of $y=f(x)$ is shown below:

    1. Sketch the graph of $y=-f(x).$

    2. Sketch the graph of $y=f(-x).$

    3. Sketch the graph of MATH

    4. Sketch the graph of MATH

  8. If $\sec \theta =4,$and MATHFind

    1. $\sin \theta .$

    2. MATH

    3. MATH

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