PRECALCULUS REVIEW SHEET FOR SECTION 1.1 – 1.3 TEST
State the property being illustrated by the equation.
1. 2(3 + x) = 2(3) + 2x _______________ 2. 2 + (x + y) = (x + y ) + 2 __________
3. 8 + 5 is a real number ______________ 4. 8 + (-8) = 0 _____________________
5. 1(n) = n __________________________ 6. 4(2n) = (4 2)n ___________________
Sketch the graph and write the interval notation for each.
7. –3 < x < 4
8. x > 9
9. 12  x
10. –3  x  5
11. Find the distance between the points (-2, 7) and (8, 3). Leave your answer in radical
form.
12. Find the midpoint of the line segment that connects the points (-4, 6) and (-3, -4).
13. Triangle ABC has vertices A(-2, 3), B(3, -4) and C(-4, 1). Prove that the triangle is
isosceles, but not equilateral.
14. Find the values of x so that the point (x, 7) is a distance of 13 spaces away from the
point (3, -5).
15. Use the graph to answer the following:
a. f(-1) = _______
b. f(2) = ________
c. f(x) = 0, x = _____
d. f(x) = 2, x = ________
Give the domain and range of each function.
x  21
16. f(x) = x2 – 40
17. f(x) =
18. f(x) = 10x3 – 400x
19. f(x) = -2 -
x3
Give the domain of each function. (Challenge yourself on the range)
x8
20. f(x) =
3x  2
x 2  6x  5
21. f(x) =
x 1
22. Sketch a function with D: [-3, 5] and R: [0, 5].
23. Sketch a function with a domain of all real numbers and range ( , 2) .
24. Prove that the triangle with vertices (1, 6), (-2, 5), and (2, 3) is a right triangle.
25. Is the triangle with vertices (-1, 4), (5, 6), and (0, 2) equilateral, isosceles, or scalene?