5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:46

78 STEP 4. Review the Knowledge You Need to Score High

Note that (a)f(x−2) is a horizontal shift off(x) by 2 units to the right, (b) f(x)+1isa

vertical shift off(x) by 1 unit upward, and (c) 2f(x) is a vertical stretch off(x) by a factor

of 2. (See Figure 5.4-22.)

2 f(x)

f(x) + 1

f(x − 2)

(^0123456)
1
2
3
4
5
6
x
y
Figure 5.4-22
5.5 Rapid Review

1. If linelis parallel to the liney− 3 x=2, findml, the slope of linel.
   Answer: ml= 3


2. If linelis perpendicular to the line 2y+x=6, findml.
   Answer: ml= 2


3. Ifx^2 +y=9, find thex-intercepts andy-intercept.
   Answer:Thex-intercepts are±3 (by settingy=0), and they-intercept is 9 (by
   settingx=0).


4. Simplify (a) ln(e^3 x) and (b)eln(2x).
   Answer:Sincey=lnxandy=exare inverse functions, ln(e^3 x)= 3 xandeln(2x)= 2 x.


5. Simplify ln

(

1

x

)

.

Answer:Since ln

(a

b

)

=ln(a)−ln(b), ln

(

1

x

)

=ln(1)−lnx=−lnx.

6. Simplify ln (x^3 ).
   Answer:Since ln(ab)=blna,ln(x^3 )=3lnx.


7. Solve the inequalityx^2 − 4 x>5, using your calculator.
   Answer:Lety 1 =x^2 − 4 xandy 2 =5. Look at the graph and see wherey 1 is abovey 2.
   Solution is{x:x<−1orx> 5 }. (See Figure 5.5-1.)