Solução_Calculo_Stewart_6e

F.
TX.10
SECTION 1.1 FOUR WAYS TO REPRESENT A FUNCTION ¤ 11
33. f(x) =5is defined for all real numbers, so the domain is R,or(−∞, ∞).
The graph of f is a horizontal line with y-intercept 5.
35. f(t) =t 2 − 6t is defined for all real numbers, so the domain is R,or
(−∞, ∞). The graph of f is a parabola opening upward since the coefficient
of t 2 is positive. To find the t-intercepts, let y =0and solve for t.
0=t 2 − 6t = t(t − 6) ⇒ t =0and t =6.Thet-coordinate of the
vertex is halfway between the t-intercepts, that is, at t =3.Since
f(3) = 3 2 − 6 · 3=−9,thevertexis(3, −9).
37. g(x) = √ x − 5 is defined when x − 5 ≥ 0 or x ≥ 5,sothedomainis[5, ∞).
Since y = √ x − 5 ⇒ y 2 = x − 5 ⇒ x = y 2 +5,weseethatg is the
tophalfofaparabola.
39. G(x) =
3x + |x|
x if x ≥ 0
.Since|x| =
x
−x if x0
if x0
if x0
2 if x