MATHEMATICS 1571

Final Examination Review Probems

  1. For the function \(f\) defined by \(f(x) = 2x^2 - 5x\) find the following:
    1. \(f(a + b)\)
    2. \(f(2x) - 2f(x)\)
  2. Find the domain of \(g\) if
    1. \(g(x) = \sqrt{x^2-3x-3} \)
    2. \(g(x) = \dfrac{x + 2}{x^3 - x}\)
  3. The graph of \(f(x) = \sqrt{x + 3} -4 \) is the same as the graph of \(f(x) = \sqrt{x} \) except that it is moved how?
  4. For the functions \(f\) and \(g\), find \(f \circ g\), \(g \circ f\), and the domains of each.
    1. \(f(x) = \dfrac{1}{x^2 - 1}\),    \(g(x) = \sqrt{x} \)
    2. \(f(x) = x^2 + 1\),    \(g(x) = \dfrac{x}{x-1} \)
  5. Find the intercepts of the following equations. Also determine whether the equations are symmetric with respect to the \(y\)-axis or the origin.
    1. \(y = x^4 + x^3 + x^2\)
    2. \(y = \dfrac{1}{x^3 - 3x} \)
    3. \(y = 2 - |x| \)