AnswersPrecalculusThe General Equation of Conic Sections

Understanding the Concept of a Limit Answers

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1
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Consider the function g(x) = . What is , if it exists?

Question illustration
A
–9
B
–1
C
7
D
DNE
2
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Review the graph of function f(x).

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

Review the graph of function h(x).

Question illustration
A
0
B
1
C
3
D
DNE
4

Review the graph of function f(x).

Question illustration
A
–4
B
–2
C
2
D
4
5

Review the table of values for function h(x).xh(x)9.912.79.9912.979.99912.9979.999912.999710undefined10.000118.500410.00118.50410.0118.5410.118.9

A
12.5
B
13
C
18.5
D
19
6

Review the table of values for function p(x).xp(x)–14.11.1–14.011.6–14.0011.96–14undefined–13.9991.97–13.991.8–13.91.76

A
1
B
1.75
C
2
D
DNE
7

Review the table of values for function g(x).xg(x)0.970.997000.99970,0000.99997,000,0001undefined1.00017,000,0001.00170,0001.017001.17

A
0
B
7,000,000
C
700,000,000
D
DNE
8

Review the table of values for function h(x).xh(x)8.93.838.99–1.198.9994.739undefined9.001–4.739.011.199.1–3.83

A
The limit does not exist because the values of h(x) seem to oscillate between random values around x = 9.
B
The limit does exist because h(x) is defined for all given values around x = 9, even though h(x) isn’t defined at x = 9.
C
The limit does not exist because h(x) is not defined at x = 9, and for a limit to exist, the function must be defined at x = 9.
D
The limit does exist because the values of h(x) to the right of x = 9 are all opposites of the values of h(x) to the left of x = 9.
9

Review the graph of function g(x).

Question illustration
A
0 0
B
DNE DNE
C
0 −2
D
DNE −2
10

Review the table of values for function g(x).xg(x)28.9–3.75128.99–3.7628.999–3.929undefined29.001–4.129.01–4.2429.1–4.249

A
–4.25
B
–4
C
–3.75
D
DNE
11

Review the graph of function f(x).

Question illustration
A
0
B
2
C
6
D
8
12

Review the graph of function g(x).

Question illustration
A
Limit of g (x) = 2 as x approaches 4 negative and limit of g (x) = negative 4 as x approaches 4 plus
Option A
B
Limit of g (x) = negative 4 as x approaches 4 negative and limit of g (x) = negative 2 as x approaches 4 plus
Option B
C
Limit of g (x) = negative 4 as x approaches 4 negative and limit of g (x) D N E as x approaches 4 plus
Option C
D
Limit of g (x) D N E as x approaches 4 negative and limit of g (x) = negative 4 as x approaches 4 plus
Option D
13

Review the graph of function f(x).

Question illustration
A
The limit = –2 because the value of the function at x = 0 is –2.
B
The limit does not exist because there is an open circle at (0, 4).
C
The limit = 4 because both the left-hand and right-hand limits equal 4.
D
The limit does not exist because there is oscillating behavior around x = 0.
14

Review the graph of function f(x), which is defined for –6 ≤ x ≤ 8.

Question illustration
A
Limit of f (x) as x approaches 2 plus
B
Limit of f (x) as x approaches 2 minus
C
Limit of f (x) as x approaches negative 6 plus
D
Limit of f (x) as x approaches negative 6 minus
15

Which graph of f(x) satisfies the conditions = –4 and = 0?

Question illustration
A
On a coordinate plane, a line starts at closed circle (2, negative 4) and goes up through (negative 2, 0). A curve starts at open circle (2, 0) and goes to open circle (4, 2). A line starts at closed circle (4, negative 2) and goes to (6, negative 2).
Option A
B
On a coordinate plane, a line starts at closed circle (0, negative 2) and goes to (negative 6, negative 2). A curve starts at open circle (0, 2) and curves down to open circle (2, 0). A line starts at closed circle (2, negative 4) and goes to (6, 0).
Option B
C
On a coordinate plane, a line starts at closed circle (2, negative 2), goes to closed circle (negative 2, negative 4), and then goes to (negative 6, 4). A curve starts at open circle (2, 0) and curves to open circle (4, 2). A line starts at closed circle (4, negative 2) and goes to (6, negative 2).
Option C
D
On a coordinate plane, a line starts at closed circle (0, negative 3), goes to closed circle (negative 2, negative 4), and then goes to (negative 6, 4). A curve starts at open circle (0, 2) and curves down to open circle (2, 0). A line starts at closed circle (2, negative 2) and goes down to (6, negative 6).
Option D
16

Review the table of values for function g(x).xg(x)32.9–732.99–6.132.999–6.0133.001–15.0133.01–15.133.1–16

A
Limit of g (x) = negative 16 as x approaches 33 minus and limit of g (x) = negative 7 as x approaches 33 plus
B
Limit of g (x) = negative 15 as x approaches 33 minus and limit of g (x) = negative 6 as x approaches 33 plus
C
Limit of g (x) = negative 7 as x approaches 33 minus and limit of g (x) = negative 16 as x approaches 33 plus
D
Limit of g (x) = negative 6 as x approaches 33 minus and limit of g (x) = negative 15 as x approaches 33 plus

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