Math 104 Pre-Calculus
Sample Test 2
In problems 1 – 2, find the - and -intercepts of the given equation.
1.
+ 2 = 8 − 4
− 2
+ + 1
= 25
2.
In problems 3 – 6, find all real solutions of the given equation.
3.
3 − 2|6 + 1| = −3
4.
32 = 8 5.
/ − 7 / + 12 = 0
6.
√ + 7 + √ + 12 = 5
In problems 7-8, solve for x:
7.
x–6<
< 3x-2
8.
|3x – 2| - 9 = 4
!
In problems 9 – 11, let = − , =
, and # = √.
"
Find each of the following functions and give the domain.
9.
% ∘ '
10.
ℎ ∘ '
11.
%) . .
12. Find the average rate of change of ' = *+, + 2 on the interval - , 0.
13. Find the average rate of change of f(x) = x2 – 2x + 1 on the interval [3, 4]
14. Find and simplify the difference quotient of the function f(x) = 3-x2. Recall that the
difference quotient is
' + ℎ − '
ℎ
15. a) Graph the piecewise function given below.
2
' = 1 9 − , < 0
1 − , ≥ 0
b) Find the interval(s) where the function is increasing and where it is decreasing.
In problems 16 – 19, graph the given function and state its domain and range using
interval notation.
16. f(x) = (x-3)2 - 5
17. f(x) = - √5 − 25 - 3
18. ' = −√1 − + 1
19. f(x) = |4x – 3| + 5
Solve for x:
20. |2x – 4| > 8
21. |1 –x | < 1
Answers: 1) y: (0, 2), (0, -2), x: (2, 0); 2) x= 2 ±2√6 , y = -1±√21 ;
3) x = -2/3, 1/3; 4) x = 0, ± 1/2 ; 5) x = ±8, ±3√3 ; 6) x= -3; 7) 13/11 < x < 5;
8) x = -11/3, 5; 9) (4x2 – 7)/(7- 2x2), x ≠ ±27/2 ; 10) 2√ 1, |x|≥ 1; 11) (3+5x)/(2+x), x≠2;
12) 4√3 / π; 13) 5, 14) -2x – h; 15b) increasing [-3, 0], decreasing x≥0; 20) x > 6 or x < -2;
21) 0<x<2
15.
16.
Domain: all reals, Range: y ≥ -5
17.
Domain: x ≥ 5, range y ≤ -3
18.
Domain |x|≤1, Range 0 ≤y≤1
19.
Domain all x, Range y ≥5
19.