Precalculus by Richard Wright

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# 1-Review

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

1. 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.
2. Graph $$f(x) = \sqrt{x+3}$$.
3. Graph f(x) = −|2x|.
4. Graph (x + 1)2 + (y − 2)2 = 16.
5. Graph f(x) = \left\{\begin{align} \tfrac{1}{2}x^2, \text{ if }x ≤ 0 \\ -|x|, \text{ if } x > 0\end{align}\right..
6. Find the equation of the line passing through (15, 20) and (17, −10).
7. Find the equation of the line parallel to y = −2x − 1 and passing through (1, 3).
8. If f(x) = 3x3 + |x|, find f(−2).
9. If $$f(x) = \frac{x}{x-1}$$, find f(x + 2).
10. Find the domain of $$f(x) = \sqrt{2x-4}$$.
11. Find the zeros of f(x) = x2 − 4.
12. Determine the intervals that f(x) = −|x + 4| is increasing and decreasing.
13. Identify the parent function of $$f(x) = \frac{2}{(x+2)^2}$$.
14. Describe how the formula is a transformation of a parent function: g(x) = −|2x| + 3.
15. Find the inverse of f(x) = (x − 2)2, x < 2.
16. If y varies directly with x, and y = 4 when x = 3, find y when x = $$\frac{3}{5}$$.
17. Use f(x) = 2x − 1 and g(x) = 4x2 to solve the following problems.

18. Find (gf)(x).
19. Find (fg)(x).
20. Find (gf)(x).
21. 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

1. $$\left(-\frac{3}{2}, \frac{7}{2}\right)$$; $$\sqrt{74}$$
2. y = −15x + 245
3. y = −2x + 5
4. −22
5. $$\frac{x+2}{x+1}$$
6. [2, ∞)
7. −2, 2
8. Increasing: (−∞, −4); Decreasing: (−4, ∞)
9. Reciprocal squared function
10. Reflected over the x-axis, Horizontal contraction by a factor of $$\frac{1}{2}$$, Vertical shift of 3
11. $$f^{-1}(x) = -\sqrt{x} + 2$$
12. $$y = \frac{4}{5}$$
13. 8x3 − 4x2
14. 8x2 − 1
15. 16x2 − 16x + 4
16. ; y = 1.5x + 6.8