The range of the given expression f(x) - d = - a√(x + c) can be determined by analyzing the effects of each term in the equation.
1. The term "f(x)" represents the function itself. Since we don't have any specific information about the function, we cannot determine its range accurately. Without knowing the function, we cannot determine the range based solely on this term.
2. The term "-d" represents a constant value. It does not affect the x-values or the square root expression, so it doesn't impact the range. Therefore, we can ignore this term when determining the range.
3. The term "-a√(x + c)" is a square root expression with a negative sign in front. The square root of a number is always non-negative (>= 0), so the negative sign will flip the sign of the result.
- For example, if we have √(x + c) = 4, then -√(x + c) = -4.
- Similarly, if √(x + c) = 0, then -√(x + c) = 0.
So, the square root expression will only produce non-positive values.
Based on this analysis, we can conclude that the range of the given expression f(x) - d = - a√(x + c) is:
B. y ≤ d
This means that the output values (y) of the function f(x) - d will be less than or equal to the value of d.