Solução_Calculo_Stewart_6e

F.
TX.10
18 ¤ CHAPTER 1 FUNCTIONS AND MODELS
7. The graph of y = f(x) = √ 3x − x 2 has been shifted 4 units to the left, reflected about the x-axis, and shifted downward
1 unit. Thus, a function describing the graph is
y = −1 ·
reflect
about x-axis
f (x +4)
shift
4 units left
− 1
shift
1 unit left
This function can be written as
y = −f(x +4)− 1=− 3(x +4)− (x +4) 2 − 1=− 3x +12− (x 2 +8x +16)− 1=− √ −x 2 − 5x − 4 − 1
9. y = −x 3 : Start with the graph of y = x 3 and reflect
about the x-axis. Note: Reflecting about the y-axis
gives the same result since substituting −x for x gives
us y =(−x) 3 = −x 3 .
11. y =(x +1) 2 : Start with the graph of y = x 2
and shift 1 unit to the left.
13. y =1+2cosx: Start with the graph of y =cosx, stretch vertically by a factor of 2,andthenshift1 unit upward.
15. y =sin(x/2): Start with the graph of y =sinx and stretch horizontally by a factor of 2.