nalyze the effect on the graph of \( f(x)=2 \sqrt{x+3}-4 \) to \( g(x)=2 \sqrt{x+8}-4 \) vith regard to the domain or range. (1 point) The range will change from \( [-4, \infty) \) to \( [4, \infty) \) The range will change from \( [3, \infty) \) to \( [8, \infty) \) The domain will change from \( [-3, \infty) \) to \( [-8, \infty) \). The domain will change from \( [3, \infty) \) to \( [8, \infty) \).

To analyze the effect on the graph, let’s break it down! The function \( f(x) = 2 \sqrt{x+3} - 4 \) has a domain of \( [-3, \infty) \) because the expression under the square root must be non-negative, which means \( x + 3 \geq 0 \). For the range, the minimum value occurs when \( x = -3 \), giving \( f(-3) = -4 \), hence the range is \( [-4, \infty) \). Now, for the function \( g(x) = 2 \sqrt{x+8} - 4 \), the domain shifts to \( [-8, \infty) \) due to the new square root expression. At \( x = -8 \), we find \( g(-8) = -4 \) as well, thus the range remains \( [-4, \infty) \). So while the domain expanded leftward, the range didn’t budge a bit!