# 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. $$y = 2 - |x|$$