Chapter Test
In Exercises 1 and 2, write an equation for the specified line.
1.
through (4, - 12) and parallel to 4 x + 3 y = 12
2.
the line y = f (x ) where f has the following values:
-2 2
x
f(x) 4 2
4
1
1
5
3. Determine whether the graph of the function y = x is
symmetric about the y -axis, the origin or neither.
4.
x4 + 1
Determine whether the function y = 3
is even, odd or neither.
x - 2x
Chapter Test
In Exercises 5 and 6, find the (a ) domain and (b) range, and
(c)graph the function.
5. y = 2sin (3 x + p )- 1
6. y = ln (x - 3)+ 1
Chapter Test
7.
Write a piecewise formula for the function.
1
1
2
Chapter Test
8.
x = 5cos t ,
y = 2sin t ,
for a curve.
0 £ t £ 2p
is a parametrization
(a ) Graph the curve.
Identify the initial and terminal points, if any.
Indicate the direction in which the curve is traced.
(b) Find a Cartesian equation for a curve that contains
the parametrized curve.
What portion of the graph of the Cartesian equation
is traced by the parametrized curve?
Chapter Test
9.
Give one parametrization for the line segment with
endpoints (- 2, 5) and (4,3).
10. Given f (x )= 2 - 3 x,
(a ) find f - 1 and show that ( f ○ f - 1 )(x)= ( f - 1 ○ f )(x )
(b) graph f and f - 1 in the same viewing window
Chapter Test Solutions
In Exercises 1 and 2, write an equation for the specified line.
4
20
1. through (4, - 12) and parallel to 4 x + 3 y = 12
y = - x3
3
2. the line y = f (x ) where f has the following values:
x
-2 2
f(x) 4
2
4
y= -
1
x+ 3
2
1
1
5
3. Determine whether the graph of the function y = x is
symmetric about the y -axis, the origin or neither.
Origin
4.
x4 + 1
Determine whether the function y = 3
is even, odd
x - 2x
or neither. Odd
Chapter Test Solutions
In Exercises 5 and 6, find the (a ) domain and (b) range, and
(c)graph the function.
5. y = 2sin (3x + p )- 1
(a ) All Reals (b) [- 3, 1]
[-π, π] by [-5, 5]
6.
y = ln (x - 3)+ 1
(a )(3, ¥ )
[- 2, 10] by [- 2, 5]
(b) All Reals
Chapter Test Solutions
7.
Write a piecewise formula for the function.
1
1
2
ìïï 1- x, 0 £ x < 1
f (x)= í
ïïî 2 - x, 1£ x £ 2
Chapter Test Solutions
8.
x = 5cos t ,
y = 2sin t ,
for a curve.
0 £ t £ 2p
is a parametrization
(a ) Graph the curve.
Identify the initial and terminal points, if any.
Indicate the direction in which the curve is traced.
Initial Point (5, 0)
Terminal Point (5, 0)
Chapter Test Solutions
8.
(b) Find a Cartesian equation for a curve that contains
2
2
æx ÷
ö æy ö÷
ç
the parametrized curve. ç ÷
+ çç ÷
=1
çè 5 ÷
ø èç 2 ø÷
What portion of the graph of the Cartesian equation
is traced by the parametrized curve? All
Chapter Test Solutions
9.
Give one parametrization for the line segment with
endpoints (- 2, 5) and (4,3). (A possible answer)
x = - 2 + 6t ,
y = 5 - 2t ,
0 £ t£ 1
10. Given f (x )= 2 - 3x,
(a ) find f - 1 and show that ( f ○ f - 1 )(x)= ( f - 1 ○ f )(x )
2- x
3
æ2 - x ö
æ2 - x ö
- 1
÷
÷
ç
f ( f (x ))= f ç
= 2 - 3çç
÷= 2 - (2 - x)= x
÷
÷
çè 3 ÷
ç
ø
è 3 ø
(a ) f - 1 (x)=
f
- 1
( f (x)) =
f
- 1
2 - (2 - 3 x) 3 x
=
=x
(2 - 3x)=
3
3
Chapter Test Solutions
10. (b) graph f and f - 1 in the same viewing window
f - 1 (x)=
f (x )= 2 - 3x
[-5, 5] by [-5, 5]
2- x
3