Absolute maximum/minimum values from graphs ?U ? se the ?following graphs to identify th?e poin? (? f any? n the?inter? al [?a. b] ?at which the function has cm absolute maximum value or an absolute minimum value.

STEP_BY_STEP SOLUTION Step_1 When an output value of a function is a maximum or a minimum over the entire domain of the function, the value is called the absolute maximum or the absolute minimum. Let f be a function with domainD and let c be a fixed constant in D. Then the output value f ) is the 1. Absolute maximum value of f on D if and only if f(x) f(c) , for all x in D. 2. Absolute minimum value of f on D if and only if f(c) f(x) , for all x in D. Step_2 Absolute extreme values _an examples; ). The domain of f(x) is all real numbers and the range is all non-negative real numbers. The graph in the figure below suggests that the function has no absolute maximum value and has an absolute minimum of 0, which occurs at x = 0. Step_3 The Absolute extreme values on a restricted domain ; 2 If the domain of f(x ) = x is restricted to [-2, 3], the corresponding range is [0, 9]. As shown below, the graph on the interval [-2, 3] sug gests that f has an absolute maximum of 9 at x = 3 and an absolute...