Question

Use the graph of f to determine each of the following(a) the domain of f(b) the range of f(c) the zero(s) of f(d) f(4)(e) the intervals on which f is increasing(n the intervals on which f is decreasing(g) the values for which fix) <= 0(h) any relative maxima or minima(i) the value(s) of × for which f(x) = 4() Is f(3) positive or negative?

Answer 1

(a) the domain of f

The domain of a function is the set of all possible inputs for the function.

(-inf, 4.5]

(b) the range of f

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually),

(-inf, 4]

(c) the zero(s) of f

The zero of a function is any replacement for the variable that will produce an answer of zero.

x = -2.5

x = 4.5

(d) f(4)

f(4) = 1

(e) the intervals on which f is increasing

(-inf, 1)

(n the intervals on which f is decreasing

(1, 4.5)

(g) the values for which f(x) <= 0

(-inf, -2.5]

x = 4.5

(h) any relative maxima or minima

Maxima

x = 1

f(1) = 4

(i) the value(s) of × for which f(x) = 4

x = 1

(h) Is f(3) positive or negative?

Positive