A function of the form \( f(x)=a b^{x} \) is modified so that the \( b \) value remains the same but the \( a \) value is increased by 2 . How do the domain and range of the new function compare to the domain and range of the original function? Check all that apply. The range stays the same. The range becomes \( y>2 \). The domain stays the same. The domain becomes \( x>2 \). The domain becomes becomes \( y \geq 2 \).

When modifying the function \( f(x) = a b^{x} \) by increasing the \( a \) value by 2 (resulting in a new function \( f_{\text{new}}(x) = (a + 2) b^{x} \)), let's analyze how the domain and range are affected: 1. **Domain:** - **Original Function:** The domain of an exponential function like \( f(x) = a b^{x} \) is all real numbers, \( \mathbb{R} \). - **Modified Function:** The modification \( (a + 2) \) does not affect the input values \( x \). Therefore, the domain remains unchanged. 2. **Range:** - **Original Function:** For \( a > 0 \) and \( b > 0 \), the range is \( (0, \infty) \). - **Modified Function:** Adding 2 to \( a \) (assuming \( a + 2 > 0 \)) scales the output by a positive factor but doesn't change the fundamental nature of the exponential growth or decay. Hence, the range remains \( (0, \infty) \). **Conclusion:** - The **domain stays the same**. - The **range stays the same**. **Therefore, the correct statements are:** - **The range stays the same.** - **The domain stays the same.** **Answer:** Both “The range stays the same” and “The domain stays the same” are correct.