Deck 2: Functions and Graphs

Question 1

Find the domain of .

A)
B)
C)
D)
E)

Answer 1

E

Question 2

Sketch the graph of the equation.

A)
B)
C)
D)
E)

Answer 2

A

Question 3

Find the domain of

A)
B)
C)
D)
E)

Answer 3

A

Question 4

Find a formula that expresses the fact that P(x, y) is a distance 2 away from the origin.

A) $x + y ^ { 2 } = 2$
B) $$x ^ { 2 } + y ^ { 2 } = 2$$
C) $$x + y = 2$$
D) $\sqrt { x + y } = 4$
E) $\sqrt { x ^ { 2 } + y ^ { 2 } } = 2$

Question 5

In exercise physiology, aerobic power P is defined in terms of maximum oxygen intake. For altitudes up to 1,800 meters, aerobic power is optimal-that is, 100%. Beyond 1,800 meters, P decreases linearly from the maximum of 100% to a value near 40% at 5,000 meters. Estimate aerobic power at the altitude of 2,400 meters.

A) 72.5%
B) 93.8%
C) 72.6%
D) 88.3%
E) 88.75%

Question 6

Find the distance d (A, B) between the points A (1, - 1) and B (8, 1).

A) 7.28
B) 6.28
C) 6.98
D) 7.78
E) 7.18

Question 7

Sketch the graph of the function.

A)
B)
C)
D)

Question 8

Find the domain of

A)
B)
C)
D)
E)

Question 9

If the point P (3, 1) is on the graph of a function f, find the corresponding point on the graph of the function $y = - 9 f ( x - 2 ) + 1$

A) $( 1 , - 3 )$
B) $( 5,10 )$
C) $( 5 , - 8 )$
D) $( 1 , - 8 )$
E) $( 6 , - 9 )$

Question 10

Find an equation of the line shown in the figure.

A)
B)
C)
D)
E)

Question 11

Find the distance d (A, B) between the points A (6, 6) and B (6, - 4).

A) 6
B) 0
C) 10
D) 4

Question 12

Find and

A)
B)
C)
D)
E)

Question 13

Find the domain of

A)
B)
C)
D)
E)

Question 14

An object is projected vertically upward with an initial velocity of ft/sec, and its distance in feet above the ground after seconds is given by the formula . If the object hits the ground after seconds, find its initial velocity in ft/sec.

A) ft/sec
B) ft/sec
C) ft/sec
D) ft/sec
E) ft/sec

Question 15

Find

A)
B)
C)
D)
E)

Question 16

Let y = f (x) be a function with domain D = [ -10, -9 ] and range R = [ -10, -7 ]. Find the domain D and range R for the function

A)
B)
C)
D)
E)

Question 17

Simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } \text {, if } h \neq 0$ for $f ( x ) = x ^ { 2 } + 4$

A) $\frac { f ( x + h ) - f ( x ) } { h } = x + h$
B) $\frac { f ( x + h ) - f ( x ) } { h } = 2 x$
C) $\frac { f ( x + h ) - f ( x ) } { h } = 2 x + h$
D) $\frac { f ( x + h ) - f ( x ) } { h } = 2 x + h + 8$
E) $\frac { f ( x + h ) - f ( x ) } { h } = 2 x + h ^ { 2 }$

Question 18

Find and

A)
B)
C)
D)
E)

Question 19

Find an equation of the line that is tangent to the circle x ² + y ² = 25 at the point P ( 3, 4 ).

A)
B)
C)
D)
E)

Question 20

Find two positive real numbers whose sum is 48 and whose product is a maximum.

A) 24 and 24
B) 44 and 4
C) 2 and 46
D) 27 and 21
E) 31 and 17

Question 21

Find a composite function form for y if: $y = 4 + \sqrt { x ^ { 2 } + 3 }$

A) $u = x ^ { 2 } , y = 4 + \sqrt [ 3 ] { u }$
B) $u = x ^ { 2 } + 3 , y = \sqrt [ 4 ] { u }$
C) $u = x ^ { 2 } + 3 , y = 4 + u$
D) $u = x ^ { 2 } + 3 , y = \sqrt { u }$
E) $u = x ^ { 2 } + 3 , y = 4 + \sqrt { u }$

Question 22

The volume of a conical pile of sand is increasing at a rate of ft ³ /min, and the height of the pile always equals the radius r of the base. Express r as a function of time t (in minutes), assuming that r = 0 when t = 0.

A)
B)
C)
D)
E)

Question 23

Several values of two functions T and S are listed in the following tables: t
0 1 2 3
T(t)
2 3 1 0
X
0 1 2 3
S(x)
1 0 3 2
Find:

A)
B)
C)
D)
E) not possible

Question 24

Find ,

A)
B)
C)
D)
E)
Chaper 2
Answer Section
MULTIPLE CHOICE