Exponential Functions – MCQs

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

Exponential Functions – MCQs
By: Prof. Dr. Fazal Rehman | Last updated: January 31, 2025