Exponential Functions – MCQs

By: Prof. Dr. Fazal Rehman Shamil | Last updated: January 31, 2025

Question 1:

\[
\text{Which of the following is the general form of an exponential function?}
\]
\[
\text{(a) } f(x) = ax^b, \quad \text{(b) } f(x) = a^x, \quad \text{(c) } f(x) = x^a, \quad \text{(d) } f(x) = a + bx
\]
Answer: B

Question 2:

\[
\text{What is the value of } f(x) = 2^x \text{ when } x = -3?
\]
\[
\text{(a) } \frac{1}{8}, \quad \text{(b) } -8, \quad \text{(c) } 8, \quad \text{(d) } \frac{1}{3}
\]
Answer: A

Question 3:

\[
\text{If } f(x) = 5^x, \text{ what is } f(2) \times f(-2)?
\]
\[
\text{(a) } 25, \quad \text{(b) } 1, \quad \text{(c) } 5, \quad \text{(d) } 0
\]
Answer: B

Question 4:

\[
\text{Which function represents exponential decay?}
\]
\[
\text{(a) } f(x) = 2^x, \quad \text{(b) } f(x) = 5^{-x}, \quad \text{(c) } f(x) = x^2, \quad \text{(d) } f(x) = -3^x
\]
Answer: B

Question 5:

\[
\text{What is the horizontal asymptote of } f(x) = 3^x – 5?
\]
\[
\text{(a) } y = 0, \quad \text{(b) } y = -5, \quad \text{(c) } y = 3, \quad \text{(d) } y = x
\]
Answer: B

Question 6:

\[
\text{Which property is true for all exponential functions of the form } f(x) = a^x \text{ when } a > 1?
\]
\[
\text{(a) } \text{Always increasing}, \quad \text{(b) } \text{Always decreasing}, \quad \text{(c) } \text{Always negative}, \quad \text{(d) } \text{Always constant}
\]
Answer: A

Question 7:

\[
\text{If } f(x) = 4^x \text{ and } g(x) = 4^{-x}, \text{ then what is } f(3) \times g(3)?
\]
\[
\text{(a) } 0, \quad \text{(b) } 1, \quad \text{(c) } 4, \quad \text{(d) } 16
\]
Answer: B

Question 8:

\[
\text{Which equation represents an exponential function?}
\]
\[
\text{(a) } y = 2^x + 3, \quad \text{(b) } y = x^3 – 2, \quad \text{(c) } y = x^2 + 4, \quad \text{(d) } y = 3x + 5
\]
Answer: A

Question 9:

\[
\text{The function } f(x) = e^x \text{ is special because:}
\]
\[
\text{(a) } f(x) \text{ is undefined}, \quad \text{(b) } f'(x) = f(x), \quad \text{(c) } f(x) = x^e, \quad \text{(d) } f(x) = 1/e^x
\]
Answer: B

Question 10:

\[
\text{What is the range of } f(x) = 2^x?
\]
\[
\text{(a) } (-\infty, \infty), \quad \text{(b) } (0, \infty), \quad \text{(c) } [0, \infty), \quad \text{(d) } (-\infty, 0)
\]
Answer: B

Question 11:

\[
\text{If } f(x) = 3^x \text{ and } g(x) = \log_3(x), \text{ then } f(g(x)) \text{ simplifies to:}
\]
\[
\text{(a) } x, \quad \text{(b) } 3x, \quad \text{(c) } 3^x, \quad \text{(d) } x^3
\]
Answer: A

Question 12:

\[
\text{If } f(x) = 5^x, \text{ what is } f(x+2)?
\]
\[
\text{(a) } 5^x + 2, \quad \text{(b) } 5^x \times 5^2, \quad \text{(c) } 5^2x, \quad \text{(d) } 5^x / 5^2
\]
Answer: B

Question 13:

\[
\text{What transformation occurs in } f(x) = 2^x \text{ if it is changed to } f(x) = 2^{x-3}?
\]
\[
\text{(a) } Shift left 3, \quad \text{(b) } Shift right 3, \quad \text{(c) } Shift up 3, \quad \text{(d) } Shift down 3
\]
Answer: B

Question 14:

\[
\text{Which equation has the same graph as } f(x) = 2^x \text{ but reflected over the x-axis?}
\]
\[
\text{(a) } f(x) = -2^x, \quad \text{(b) } f(x) = 2^{-x}, \quad \text{(c) } f(x) = 2x, \quad \text{(d) } f(x) = -x^2
\]
Answer: A

Question 15:

\[
\text{If } g(x) = a^x \text{ has a y-intercept at (0,1), what is the value of } a?
\]
\[
\text{(a) } 1, \quad \text{(b) } 2, \quad \text{(c) } e, \quad \text{(d) } Any positive number except 0
\]
Answer: D

More MCQs on Algebra (Collected from Past Papers)

  1. Elementary Algebra – MCQs
  2. Algebraic Expressions – MCQs
  3. Algebraic Identities – MCQs
  4. Commutative Algebra – MCQs
  5. Linear Equations – MCQs
  6. Graphing Linear Equations – MCQs
  7. Inequalities in Algebra – MCQs
  8. Absolute Value Inequalities – MCQs
  9. Exponent – MCQs
  10. Exponential Functions – MCQs
  11. Logarithms – MCQs
  12. Polynomials – MCQs
  13. Factoring Methods – MCQs
  14. Polynomial Arithmetic – MCQs
  15. Quadratic Equation – MCQs
  16. Linear Algebra – MCQs
  17. Matrices in Algebra – MCQs
  18. Functions in Algebra – MCQs
  19. Sequences in Algebra – MCQs
  20. Arithmetic in Algebra – MCQs
  21. Combining Like Terms in Algebra – MCQs
  22. Abstract Algebra – MCQs
  23. Sets in Algebra – MCQs
  24. Algebra Calculator – MCQs

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