UNIT # 01 Functions and Limits 

Each question has four possible answer. Tick the correct answer. 

1. The function 𝑰(𝒙) = 𝒙 is called : 

(a) A linear function (b) ✔ An identity function (c) A quadratic function (d) A cubic function 

2. If 𝒚 is expressed in terms of a variable 𝒙 as 𝒚 = 𝒇(𝒙), then 𝒚 is called : 

(a) ✔An explicit function (b) An implicit function (c) A linear function (d) An identity function

3. 𝑪𝒐𝒔𝒉𝟐𝒙 − 𝑺𝒊𝒏𝒉

𝟐𝒙 =

(a) -1 (b) 0 (c) ✔1 (d) None of these 

4. 𝒄𝒐𝒔𝒆𝒄𝒉𝒙 is equal to 

(a) 2

𝑒

𝑥+𝑒−𝑥 (b) 1

𝑒

𝑥−𝑒−𝑥 (c) ✔

2

𝑒

𝑥−𝑒−𝑥 (d) 2

𝑒−𝑥+𝑒𝑥

5. 𝐥𝐢𝐦𝒙→𝒂

𝒙

𝟑−𝒂𝟑

𝒙−𝒂

=

(a) Undefined (b) ✔ 3𝑎2

 (c) 𝑎

2

 (d) 0 

6. 𝐥𝐢𝐦𝒙→𝟎(𝟏 + 𝒙)

𝟏

𝒙 =

(a) 1

𝑒

 (b) ✔ 𝑒 (c) 𝑒

2

 (d) Undefined 

7. The notation 𝒚 = 𝒇(𝒙) was invented by 

(a) Lebnitz (b) ✔ Euler (c) Newton (d) Lagrange 

8. If 𝒇(𝒙) = 𝒙𝟐 − 𝟐𝒙 + 𝟏 , then 𝒇(𝟎) =

(a) -1 (b) 0 (c) ✔ 1 (d) 2 

9. When we say that 𝒇 is function from set 𝑿 to set 𝒀, then 𝑿 is called 

(a) ✔Domain of 𝑓 (b) Range of 𝑓 (c) Codomain of 𝑓 (d) None of these 

10. The term “Function” was recognized by______ to describe the dependence of one quantity 

to another. 

(a) ✔Lebnitz (b) Euler (c) Newton (d) Lagrange 

11. If 𝒇(𝒙) = 𝒙𝟐

 then the range of 𝒇 is

(a) ✔ [0,∞) (b) (-∞, 0] (c) (0, ∞) (d) None of these 

12. If 𝒇(𝒙) =

𝒙

𝒙

𝟐−𝟒

 then domain of 𝒇 is

(a) 𝑅 (b) 𝑅 − {0} (c) ✔ 𝑅 − {±2} (d) 𝑄

13. If a graph express a function , then a vertical line must cut the graph at 

(a) ✔One point only (b) Two points (c) More than one point (d) No point 

14. If 𝒇(𝒙) = {

𝒙 , 𝒘𝒉𝒆𝒏𝟎 ≤ 𝒙 ≤ 𝟏

𝒙 − 𝟏 , 𝒘𝒉𝒆𝒏 𝟏 < 𝑥 ≤ 2 , then domain of 𝒇

(a) ✔ [0,2] (b) (0,2) (c) [1,2] (d) all real numbers 

15. The graph of linear equation is always a 

(a) ✔Straight line (b) parabola (c) circle (d) cube 

16. The domain and range of identity function , 𝑰: 𝑿 → 𝑿 is

(a) ✔𝑋 (b) +iv real numbers (c) –iv real numbers (d) integers 

17. The linear function 𝒇(𝒙) = 𝒂𝒙 + 𝒃 is identity function if 

(a) 𝑎 ≠ 0, 𝑏 = 1 (b) 𝑎 = 1, 𝑏 = 0 (c) 𝑎 = 1, 𝑏 = 1 (d) 𝑎 = 0

18. The linear function 𝒇(𝒙) = 𝒂𝒙 + 𝒃 is constant function if 

𝑎 ≠ 0, 𝑏 = 1 (b) 𝑎 = 1, 𝑏 = 0 (c) 𝑎 = 1, 𝑏 = 1 (d) ✔ 𝑎 = 0

19. If 𝒚 = 𝒄𝒐𝒔𝒙 , 𝒅𝒐𝒎𝒂𝒊𝒏 = 𝑹 then range is 

(a) ]-1,1[ (b) ✔ [-1,1] (c) 𝑅-[-1,1] (d) 𝑅 −]-1,1[ 

20. If 𝒚 = 𝒕𝒂𝒏𝒙, 𝒅𝒐𝒎𝒂𝒊𝒏 = {𝒙|𝒙 ∈ 𝑹, 𝒙 ≠ (𝟐𝒏 + 𝟏)

𝝅

𝟐

 , 𝒏 𝒊𝒏𝒕𝒆𝒓𝒈𝒆𝒓} then range is 

(a) ]-1,1[ (b) [-1,1[ (c) 𝑅-[-1,1] (d) ✔ all real numbers 

21. If 𝒚 = 𝒔𝒆𝒄𝒙 , 𝒅𝒐𝒎𝒂𝒊𝒏 = {𝒙|𝒙 ∈ 𝑹, 𝒙 ≠ (𝟐𝒏 + 𝟏)

𝝅

𝟐

 , 𝒏 𝒊𝒏𝒕𝒆𝒓𝒈𝒆𝒓} then range is

(a) ]-1,1[ (b) [-1,1[ (c) 𝑅-[-1,1] (d) ✔ 𝑅 −]-1,1[ 

22. If 𝒚 = 𝒄𝒐𝒕𝒙 , 𝒅𝒐𝒎𝒂𝒊𝒏 = {𝒙|𝒙 ∈ 𝑹, 𝒙 = 𝒏𝝅 , 𝒏 𝒊𝒏𝒕𝒆𝒈𝒆𝒓} then range is

(a) 𝑦 ≥ 1, 𝑦 ≤ −1 (b) 𝑦 ≤ 1, 𝑦 ≥ −1 (c) 𝑦 < 1, 𝑦 > −1 (d) ✔ all real numbers 

23. If 𝒚 = 𝒄𝒐𝒔𝒆𝒄𝒙 , 𝒅𝒐𝒎𝒂𝒊𝒏 = {𝒙|𝒙 ∈ 𝑹, 𝒙 = 𝒏𝝅 , 𝒏 𝒊𝒏𝒕𝒆𝒈𝒆𝒓} then range is

(a) ✔𝑦 ≥ 1, 𝑦 ≤ −1 (b) 𝑦 ≤ 1, 𝑦 ≥ −1 (c) 𝑦 < 1, 𝑦 > −1 (d) all real numbers