# Limit of a Function

Topics: Function, Limit of a function, Rational function Pages: 11 (1346 words) Published: November 15, 2012
Pre-Calculus – Mid-Term Name_________________

1. What is the solution region to the following function?

f (x) > 2x + 4 + 3

2. Determine which of the following relations is not a function.

A. B.

C.D.

3. Which defines the range of the following function: f (x) = x – 5

A. f (x) < 5

B. f (x) > –5

C. f (x) ≤ 5

D. f (x) ≥ –5

4. Write as one logarithm: 2log2x + 4log2y - 3log2z

A. log2xyz

B. log2x2 y4 z3

C. log2
z3

D.logxy

5. Which graph is a translation up and to the left of the parent function f (x) = – x

B. B.

C.D.

6. The solutions to the following inequality are contained in which quadrants?

2(y + x) – 5 < 5(y + x) – 14

A. I, II and IIIB. I, III and IV
C. I, II and IVD .II, III and IV

7. Which function models a translation 10 units down and 5 units right of the parent function f (x) = x

A.f (x) = 5x – 10

B.f (x) = – 10x + 5

C.f (x) = x + 10 – 5

D.f (x) = x – 5 – 10

8.You have a final project for one of your courses. You have created a one-page title page, a one-page abstract, a one page table of contents, a 20 page body report, a one page summary, 7 pages of Appendices, and a one page bibliography. Your printer requires 2.3 minutes to print 8 full pages of text at best quality mode. At this same rate, approximately how many minutes will the printer require to print your entire project at best quality mode?

A. 17
B. 32
C. 9
D. 6

9. { f (x) = –[pic]x + 3 } is perpendicular and has the same y-intercept as: A. y + 20 = x + 26
B. 2y + 20 = 10x + 26
C. 2y = 10x
D. y = 5x + 5

10. Describe the translation of the following graphs if f (x) is the original function.

A. g(x) has been translated 3 units up and 4 units left to form f (x).

B. f (x) has been translated 4 units up and 3 units left to form g(x).

C. g(x) has been translated 4 units down and 3 units right to form f (x).

D. f (x) has been translated 3 units down and 4 units right to form g(x).

11. The solutions to the following system are contained in which quadrants?

y > 2x + 5
y < –[pic]x – 3

A. II and IIIB. I, II, and III
C. I, II and IVD .II, III and IV

12.If f (x) = x2 + x , and g(x) = x3 + 2x – 1 , find

A. 35.5
B. 69.75
C. – 55
D. – 18.25

13. Define the domain and range of the following piece-wise function: y

x

A. Domain: (– 4 < x < 4 )B.Domain: (–3, –2, –1, 0 ) Range: (–3, –2, –1, 0 ) Range: (– 4 < y ≤ 4 )

C.Domain: (– 4 < x ≤ 4 )D.Domain: (–3, –2, –1, 0 ) Range: (–3, –2, –1, 0 ) Range: (– 4 < y < 4 )

14. The expression x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5 is the expansion of which of the following binomials?

A. (x + y)6B.(x + y)5

(x – y)5D.(x – y)6

15. Determine the horizontal asymptote of the following function:...