Precalculus by Richard Wright

We love because he first loved us. 1 John 4:19 NIV

Take this test as you would take a test in class. When you are finished, check your work against the answers.

- Plot the points (−5, 1) and (2, 6). Find the coordinates of the midpoint of the line segment joining the points and the distance between the points.
- Graph \(f(x) = \sqrt{x+3}\).
- Graph
*f*(*x*) = −|2*x*|. - Graph (
*x*+ 1)^{2}+ (*y*− 2)^{2}= 16. - Graph \(f(x) = \left\{\begin{align} \tfrac{1}{2}x^2, \text{ if }x ≤ 0 \\ -|x|, \text{ if } x > 0\end{align}\right.\).
- Find the equation of the line passing through (15, 20) and (17, −10).
- Find the equation of the line parallel to
*y*= −2*x*− 1 and passing through (1, 3). - If
*f*(*x*) = 3*x*^{3}+ |*x*|, find*f*(−2). - If \(f(x) = \frac{x}{x-1}\), find
*f*(*x*+ 2). - Find the domain of \(f(x) = \sqrt{2x-4}\).
- Find the zeros of
*f*(*x*) =*x*^{2}− 4. - Determine the intervals that
*f*(*x*) = −|*x*+ 4| is increasing and decreasing. - Identify the parent function of \(f(x) = \frac{2}{(x+2)^2}\).
- Describe how the formula is a transformation of a parent function:
*g*(*x*) = −|2*x*| + 3. - Find the inverse of
*f*(*x*) = (*x*− 2)^{2},*x*< 2. - If
*y*varies directly with*x*, and*y*= 4 when*x*= 3, find*y*when*x*= \(\frac{3}{5}\). - Find (
*gf*)(*x*). - Find (
*f*∘*g*)(*x*). - Find (
*g*∘*f*)(*x*). - For the following data set, draw a scatter plot and then use technology to find the equation of the best fitting line.

2 4 6 8 10 10 13 15 19 22

Use *f*(*x*) = 2*x* − 1 and *g*(*x*) = 4*x*^{2} to solve the following problems.

- \(\left(-\frac{3}{2}, \frac{7}{2}\right)\); \(\sqrt{74}\)
*y*= −15*x*+ 245*y*= −2*x*+ 5- −22
- \(\frac{x+2}{x+1}\)
- [2, ∞)
- −2, 2
- Increasing: (−∞, −4); Decreasing: (−4, ∞)
- Reciprocal squared function
- Reflected over the
*x*-axis, Horizontal contraction by a factor of \(\frac{1}{2}\), Vertical shift of 3 - \(f^{-1}(x) = -\sqrt{x} + 2\)
- \(y = \frac{4}{5}\)
- 8
*x*^{3}− 4*x*^{2} - 8
*x*^{2}− 1 - 16
*x*^{2}− 16*x*+ 4 - ;
*y*= 1.5*x*+ 6.8