The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.
- Since (5/2)^x is always greater than 0 for any x, the minimum value of f(x) is -5.
To find the maximum value of f(x), we can take the limit as x approaches infinity:
- lim (x → ∞) (5/2)^x - 5 = ∞ - 5 = ∞
Therefore, the range of f(x) is (-5, ∞).