Question

What is the range of the function f(x)=−∣x−4∣+5? a) (−, 5](−, 5] b) (−,5)(−, 5) c) [−5,)[−5,) d) [5,)[5,)

Answer 1

The range of the function f(x) = −∣x - 4∣ + 5 is (−∞, 5]

Step-by-step explanation:

The range of the function f(x) = −∣x - 4∣ + 5 is (−∞, 5]. The absolute value function ∣x - 4∣ can only output non-negative values because it always returns the distance from x to 4, which is always positive or zero. Therefore, the maximum value of -∣x - 4∣ is 0, and when we add 5 to it, the maximum value of f(x) becomes 5. Since there is no upper bound on the input x, the range extends to negative infinity.