# MATHEMATICS 1571

## Final Examination Review Probems

- For the function \(f\) defined by \(f(x) = 2x^2 - 5x\) find the following:
- \(f(a + b)\)
- \(f(2x) - 2f(x)\)

- Find the domain of \(g\) if
- \(g(x) = \sqrt{x^2-3x-3} \)
- \(g(x) = \dfrac{x + 2}{x^3 - x}\)

- 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?
- For the functions \(f\) and \(g\), find \(f \circ g\), \(g \circ f\), and the domains of each.
- \(f(x) = \dfrac{1}{x^2 - 1}\), \(g(x) = \sqrt{x} \)
- \(f(x) = x^2 + 1\), \(g(x) = \dfrac{x}{x-1} \)

- Find the intercepts of the following equations. Also determine whether the equations are symmetric with respect to the \(y\)-axis or the origin.
- \(y = x^4 + x^3 + x^2\)
- \(y = \dfrac{1}{x^3 - 3x} \)
- \(y = 2 - |x| \)