2nd Year Mathematics Chapter 1 Test01: Functions and Graphs

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

1. The logarithmic function $f(x) = \log_b x$
   1. all real numbers
   2. x < 0
   3. x > 0
   4. x ≥ 0
2. Scaling refers to:
   1. increasing the size of an object.
   2. decreasing the size of an object.
   3. maintaining the properties while resizing an object.
   4. changing the shape of an object.
3. Which of the following is an example of exponential growth function?
   1. f(x) = 3x + 4
   2. $f(x) = 3^x \times 5$
   3. f(x) = x³
   4. f(x) = x²
4. The function f: R → [0 , ∞) defined by f(x) = x²+ 1, is:
   1. onto but not one-to-one
   2. one-to-one but not onto
   3. neither one-to-one nor onto
   4. both one-to-one and onto
5. The exponential decay function is expressed by:
   1. $f(x) = a⋅ b^x; 0 < b < 1$
   2. $f(x) = a⋅ b^x; b > 1$
   3. $f(x) = a⋅ b^x ; 0 < a < 1$
   4. $f(x) = a⋅ b^x; a > 1$
6. What is the effect on the graph of f(x) when it is replaced by f(x + 2)?
   1. It shifts 2 units to the right
   2. It shifts 2 units to the left
   3. It shifts 2 units up
   4. It shifts 2 units down
7. A function f: A → B has an inverse if and only if:
   1. f is one-to-one
   2. f is onto
   3. f is both one-to-one and onto
   4. f is neither one-to-one nor onto
8. The function f(x) = x + 1, where f: {1, 2, 3} → {2, 3, 4} is:
   1. one-to-one but not onto
   2. onto but not one-to-one
   3. both one-to-one and onto
   4. neither one-to-one nor onto
9. A function f: A → B is said to be onto if:
   1. Every element of set A has a unique image in set B.
   2. Every element in set B has a preimage in set A
   3. Some elements of set B have no preimage in set A.
   4. f is both one-to-one and onto.
10. The inverse function of $f(x) = \frac{1}{x} ; x \neq 0$, is:
    1. $f^{-1}(x) = 1$
    2. $f^{-1}(x) = - x$
    3. $f^{-1}(x) = -x$
    4. $f^{-1}(x) = \frac{1}{x}$