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- Solve for x: −2(1 − x) + 2 = 3x + 1.
a) x = − (^15) b) x = − (^12) c) x = − (^14) d) x = − 1 e) x = − 3
- Find all real solutions of the equation x + 3√x − 4 = 0.
a) x = − 4 b) x = 4; x = − 1 c) x = − 1 d) x = −4; x = 1 e) x = 1
- Solve for x: (^) √ x − 1 − 2 = x − 9.
a) x = 10, x = 5 b) x = 10, x = − 5 c) 10 d) No solution e) 5
- Solve for x: 2 | 3 x − 1 | ≤ 8.
a) [− 3 , 2] b) (−∞, −1] ∪
[ 5
3 ,^ ∞
c)
]
∪ [2, ∞)
d)
[
]
e)
[
]
- Solve the inequality^3 xx + 4+ 6 > 2.
a) (− 4 , 2) b) (−∞, −4) ∪ (2, ∞) c) (−∞, −2) ∪ (4, ∞) d) (− 2 , 4) e) (2, ∞)
- Which of the following functions has a relative maximum? a) −x^4 b) | x − 2 | c) log 2 (x) d) e−x e) √1 + x
- Given the piecewise-defined function
f (x) =
√x + 2, if x ≥ 1 −x^2 , if − 1 ≤ x < 1 |x + 1| , if x < − 1
determine which of the following statements is TRUE.
a) f is increasing on (0, ∞) b) f is constant on (−∞, −1) c) x = −2 is an x-intercept d) f (−1) = − 1 e) at x = 0, f has a relative minimum
- Given the function f (x) =^1 x , find and simplify f^ (x^ +^ h h)^ −^ f^ (x).
a) (^) h^12 b) (^) x(x 1 + h)
c) − (^) x^12 d) − (^) x(x 1 + h)
e) − (^) x(xh + h)
- Find (f ◦ f ) (0), where
f (x) =
x^2 + 1 if x < 0 (^2) √ if x = 0 x + 2 − x^2 if 0 < x ≤ 2 16 /x^2 if x > 2
a) − 2 b) 0 c) 4 d) √ 3 − 1 e) 16
- Find the inverse function of f (x) =^5 − 7 x^9 x.
a) 5 + 7 9 x b) (^9) −^5 7 x
c) 57 x − 9 d) (^7) x 5 + 9
e) 5 − 9 7 x
- Which of the following functions is one-to-one?
a) f (x) = 7|x| b) f (x) =^25
c) f (x) =
{ − 5 x if x < 0 2 − x ifx > 2 d) f (x) = x^2 (x − 1)(x − 2) e) f (x) = −x^3 (x − 1)
- A projectile is launched vertically from the ground into the air with initial velocity v 0. It reaches the ground in 10 minutes. Assume that the height of the projectile above the ground after t minutes is given by h(t) = − 5 t^2 + v 0 t. Find the initial velocity v 0 of the projectile.
a) 100 b) 0 c) undefined d) 25 e) 50
- Match the graph with one of the given functions:
a) f (x) = −(x + 3)(x + 1)(x − 2)^2 b) f (x) =^12 (x + 2)^2 (x − 1)(x + 3) c) f (x) =^12 (x + 3)(x + 1)(x − 2)^2 d) f (x) = 2(x + 3)^2 (x − 2)x e) f (x) =^14 (x − 2)^4 (x + 1)^2 (x − 3)
- Give the REMAINDER of 2 x^3 + 7x^2 + 2x − 3 x + 3. a) 1 b) − 3 c) 3 d) − 1 e) 0
- Find all vertical asymptotes of the graph of f (x) = 2 −xx (^22) −^ − 2 xx^ + 6− 4.
a) x = −1, x = 2 b) x = − 3 , x = 2 c) y = − 3 , y = 2 d) x = − 1 e) The graph has no vertical asymptotes
- Solve for x: 32 x+1^ = 7x
a) x = (^2) −ln(3) ln(7)
b) x = (^) ln(3)ln(7) − 2
c) x = (^) ln(7)ln(3) − 2 ln(3)
d) x =^2 −ln(3)^ ln(7)
e) x = ln(3)ln(7)^ −^2
1. D
2. E
3. C
4. E
5. B
6. A
7. D
8. D
9. A
10. D
11. C
12. E
13. C
14. E
15. D
16. C
17. A
18. D
19. C
20. B
21. E
22. D
23. C
24. C
25. C
