Solução_Calculo_Stewart_6e

F.
TX.10
14 ¤ CHAPTER 1 FUNCTIONS AND MODELS
5. (a) An equation for the family of linear functions with slope 2
is y = f(x) =2x + b,whereb is the y-intercept.
(b) f(2) = 1 means that the point (2, 1) is on the graph of f. We can use the
point-slope form of a line to obtain an equation for the family of linear
functions through the point (2, 1). y − 1=m(x − 2), which is equivalent
to y = mx +(1− 2m) in slope-intercept form.
(c) To belong to both families, an equation must have slope m =2, so the equation in part (b), y = mx +(1− 2m),
becomes y =2x − 3. Itistheonly function that belongs to both families.
7. All members of the family of linear functions f(x) =c − x have graphs
that are lines with slope −1. They-intercept is c.
9. Since f(−1) = f(0) = f(2) = 0, f has zeros of −1, 0,and2,soanequationforf is f(x) =a[x − (−1)](x − 0)(x − 2),
or f(x) =ax(x +1)(x − 2). Because f(1) = 6, we’ll substitute 1 for x and 6 for f(x).
6=a(1)(2)(−1) ⇒ −2a =6 ⇒ a = −3, so an equation for f is f(x) =−3x(x +1)(x − 2).
11. (a) D =200,soc =0.0417D(a +1)=0.0417(200)(a +1)=8.34a +8.34. The slope is 8.34, which represents the
change in mg of the dosage for a child for each change of 1 year in age.
(b) For a newborn, a =0,soc =8.34 mg.
13. (a) (b) The slope of 9 means that F increases 9 degrees for each increase
5 5
of 1 ◦ C. (Equivalently, F increases by 9 when C increases by 5
and F decreases by 9 when C decreases by 5.) The F -intercept of
32 is the Fahrenheit temperature corresponding to a Celsius
temperature of 0.