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

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

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

g(x)

(^0123)
1
2
3
x
y
Figure 5.6-2

10. Find the inverse of the functionf(x)=x^3 + 1.


11. Sketch the graph of the equation
    y=3 cos

(

1

2

x

)

in the interval

− 2 π≤x≤ 2 πand indicate the

amplitude, frequency, and period.

12. On the same set of axes, sketch the
    graphs of:
    (1)y=lnx (2)y=ln(−x)
    (3)y=−ln(x+3)

Part B Calculators are permitted.

13. Solve the inequality| 2 x+ 4 |≤10.


14. Solve the inequalityx^3 − 2 x>1.


15. Evaluate tan

(

arccos

√

2

2

)

.

16. Solve forxto the nearest thousandth:
    e^2 x− 6 ex+ 5 =0.


17. Solve forxto the nearest thousandth:
    3ln2x− 3 =12.


18. Solve the inequality
    2 x− 1
    x+ 1

≤1.

19. Determine if the function
    f(x)=− 2 x^4 +x^2 +5 is even, odd, or
    neither.


20. Given the functionf(x)=x^4 − 4 x^3 ,
    determine the intervals over which the
    function is increasing, decreasing, or
    constant. Find all zeros of f(x), and
    indicate any relative minimum and
    maximum values of the function.

5.7 Cumulative Review Problems

21. Given a linear functiony=f(x), with
    f(2)=4 and f(−4)=10, find f(x).


22. Solve the inequalityx^3 −x≥ 0
    graphically.


23. Iff(x)=

1

x

,x =0, evaluate

f(x+h)− f(x)

h

and express the answer

in simplest form.

24. Giveng(x)= 3 x−12, findg−^1 (3).


25. Write an equation of the tangent line to
    the graph ofx^2 +y^2 =25 at the point
    (4,−3).

5.8 Solutions to Practice Problems

Part A The use of a calculator is not

allowed.

1. Rewrite the equation 3x− 4 y+ 12 = 0
   iny=mx+bform:y =

3

4

x+3. Thus,

the slope of the line is

3

4

. Since linelis

parallel to this line, the slope of linel

must also be

3

4

. Linelalso passes
through the point (−2, 5). Therefore, an
equation of linelisy− 5 =

3

4

(x+2).

2. LetMbe the midpoint ofBC. Using the
   midpoint formula, you will find the