Which statement best describes the transformations applied to $f(x) = 2^x$ to obtain $g(x) = -3 \cdot 2^{x+5} + 8$?

Reflected over the x-axis, vertically stretched by a factor of 3, shifted 5 units left, and shifted 8 units up.

Reflected over the x-axis, vertically stretched by a factor of 3, shifted 5 units right, and shifted 8 units up.

Vertically stretched by a factor of 3, shifted 5 units left, and shifted 8 units down.

Reflected over the y-axis, vertically compressed by a factor of $\frac{1}{3}$, shifted 5 units left, and shifted 8 units up.

The function $f(x)=6^x$ is transformed by a vertical compression of factor $\frac{1}{4}$, a shift 2 units right, and a shift 9 units down. What is the resulting function $g(x)$?

$g(x) = \frac{1}{4} \cdot 6^{x-2} - 9$

$g(x) = \frac{1}{4} \cdot 6^{x+2} + 9$

$g(x) = \frac{1}{4} \cdot 6^{x-9} - 2$

Exponential Functions Practice — Grade 8 math

Lesson 3: Exponential Functions — Practice Questions

1. What is the equation of the horizontal asymptote for the function $g(x) = 5 \cdot 4^{x-2} - 6$? The equation should be in the form $y = \_\_\_$.
2. Which statement best describes the transformations applied to $f(x) = 2^x$ to obtain $g(x) = -3 \cdot 2^{x+5} + 8$?
- A. Reflected over the x-axis, vertically stretched by a factor of 3, shifted 5 units left, and shifted 8 units up.
- B. Reflected over the x-axis, vertically stretched by a factor of 3, shifted 5 units right, and shifted 8 units up.
- C. Vertically stretched by a factor of 3, shifted 5 units left, and shifted 8 units down.
- D. Reflected over the y-axis, vertically compressed by a factor of $\frac{1}{3}$, shifted 5 units left, and shifted 8 units up.
3. The function $f(x)=6^x$ is transformed by a vertical compression of factor $\frac{1}{4}$, a shift 2 units right, and a shift 9 units down. What is the resulting function $g(x)$?
- A. $g(x) = \frac{1}{4} \cdot 6^{x-2} - 9$
- B. $g(x) = 4 \cdot 6^{x+2} - 9$
- C. $g(x) = \frac{1}{4} \cdot 6^{x+2} + 9$
- D. $g(x) = \frac{1}{4} \cdot 6^{x-9} - 2$
4. Which of the following is an exponential function?
- A. $f(x) = x^4$
- B. $g(x) = 1^x$
- C. $h(x) = (-2)^x$
- D. $k(x) = 4^x$
5. The function $f(x) = 8^{-x}$ can be rewritten as an exponential function in the form $b^x$. What is the value of the base $b$? ___
6. Which of the following values could not be the base of an exponential function?
- A. 10
- B. 1
- C. $\frac{1}{2}$
- D. 3
7. For the exponential function $g(x) = (\frac{2}{5})^x$, the value of the base $b$ is ___.
8. Is the function $f(x) = (\frac{1}{7})^{-x}$ an exponential function?
- A. Yes
- B. No