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

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

Review of Precalculus 79

ToolsF1 TraceF3

MAIN RAD AUTO FUNC

ZoomF2 ReGraphF4 MathF5 DrawF6 F7Pen

[−2, 6] by [−5, 10]

Figure 5.5-1

8. Evaluate sin

(

π

6

)

, tan

(

π

4

)

, and cos

(

π

6

)

.

Answer:sin

(

π

6

)

=

1

2

, tan

(

π

4

)

=1, and cos

(

π

6

)

=

√

3

2

.

9. f(x)=

√

x^2 − 1

x− 2

.

Answer:The domain off is{x:|x|≥1 andx = 2 }.

10. Is the functionf(x)=x^4 −x^2 even, odd, or neither?
    Answer: f(x) is an even function since the exponents ofxare all even.

5.6 Practice Problems

Part A The use of a calculator is not allowed.

1. Write an equation of a line passing
   through the point (−2, 5) and parallel to
   the line 3x− 4 y+ 12 =0.


2. The vertices of a triangle areA(−2, 0),
   B(0, 6), andC(4, 0). Find an equation of
   a line containing the median from vertexA
   toBC.


3. Write an equation of a circle whose center
   is at (2,−3) and tangent to the liney=−1.


4. Solve forx:|x− 2 |= 2 x+5.


5. Solve the inequality| 6 − 3 x|<18 and
   sketch the solution on the real number line.


6. Givenf(x)=x^2 + 3 x, find
   f(x+h)− f(x)
   h
   in simplest form.


7. Determine which of the following
   equations representyas a function ofx:

(1)xy=− 8 (2) 4x^2 + 9 y^2 = 36

(3) 3x^2 −y=1 (4)y^2 −x^2 = 4

8. Iff(x)=x^2 andg(x)=

√

25 −x^2 , find

(f◦g)(x) and indicate its domain.

9. Given the graphs off andgin Figures
   5.6-1 and 5.6-2, evaluate:
   (1) (f−g)(2) (2) (f◦g)(1) (3) (g◦f )(0)

f(x)

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