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Modern Analytic Geometry

William Wooton, Edwin F. Beckenbach, Frank J. Fleming

Chapter 6

Curve Sketching - all with Video Answers

Educators

Section 1

Polynomial Functions

Problem 1

In Exercises 1-10, The given equation defines a function whose graph has one of the following general shapes. In each case, identify the appropriate shape or shapes. (In some cases, there may be two possibilities.) GRAPH CAN'T COPY.
$F(x)=-2 x^4+x^2-3 x+2$

Check back soon!
00:50

Problem 2

The given equation defines a function whose graph has one of the following general shapes. In each case, identify the appropriate shape or shapes. (In some cases, there may be two possibilities.) GRAPH CAN'T COPY.
$G(x)=5 x^3-2 x^2+3 x-1$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:52

Problem 3

The given equation defines a function whose graph has one of the following general shapes. In each case, identify the appropriate shape or shapes. (In some cases, there may be two possibilities.) GRAPH CAN'T COPY.
$H(x)=2 x^5-3 x^2+x-5$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:31

Problem 4

The given equation defines a function whose graph has one of the following general shapes. In each case, identify the appropriate shape or shapes. (In some cases, there may be two possibilities.) GRAPH CAN'T COPY.
$F(x)=-4 x^3+3 x^2-2 x+1$

AG
Ankit Gupta
Numerade Educator
00:50

Problem 5

The given equation defines a function whose graph has one of the following general shapes. In each case, identify the appropriate shape or shapes. (In some cases, there may be two possibilities.) GRAPH CAN'T COPY.
$G(x)=-x^5+2 x^3+x^2-3$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:15

Problem 6

The given equation defines a function whose graph has one of the following general shapes. In each case, identify the appropriate shape or shapes. (In some cases, there may be two possibilities.) GRAPH CAN'T COPY.
$H(x)=x^4-2 x^3+3 x^2-2 x+1$

Yuou Sun
Yuou Sun
Numerade Educator
00:59

Problem 7

The given equation defines a function whose graph has one of the following general shapes. In each case, identify the appropriate shape or shapes. (In some cases, there may be two possibilities.) GRAPH CAN'T COPY.
$F(x)=\frac{1}{2} x^3-3 x^2+2 x+1$

Calin Lupas
Calin Lupas
Numerade Educator
00:50

Problem 8

The given equation defines a function whose graph has one of the following general shapes. In each case, identify the appropriate shape or shapes. (In some cases, there may be two possibilities.) GRAPH CAN'T COPY.
$G(x)=-\frac{2}{3} x^5+x^4-3 x^3+2$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:08

Problem 9

The given equation defines a function whose graph has one of the following general shapes. In each case, identify the appropriate shape or shapes. (In some cases, there may be two possibilities.) GRAPH CAN'T COPY.
$H(x)=4 x^4+x^3-2 x^2+3 x$

Calin Lupas
Calin Lupas
Numerade Educator
01:29

Problem 10

The given equation defines a function whose graph has one of the following general shapes. In each case, identify the appropriate shape or shapes. (In some cases, there may be two possibilities.) GRAPH CAN'T COPY.
$J(x)=2 x^5-3 x^4+2 x^2-5 x+1$

Demi Nelson
Demi Nelson
Numerade Educator
01:06

Problem 11

In Exercises 11-26, Sketch the graph of the function defined by the given equation.
$f(x)=x^3$

Sara Sasani
Sara Sasani
Numerade Educator
02:11

Problem 12

Sketch the graph of the function defined by the given equation.
$g(x)=-2 x^3$

Eric Mockensturm
Eric Mockensturm
Numerade Educator

Problem 13

Sketch the graph of the function defined by the given equation.
$f(x)=x^2-x^3$

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01:34

Problem 14

Sketch the graph of the function defined by the given equation.
$g(x)=\frac{1}{4}\left(x^3-x^2\right)$

Brandon Cleary
Brandon Cleary
Numerade Educator
00:25

Problem 15

Sketch the graph of the function defined by the given equation.
$F(x)=x^3-4 x^2+3 x$

AG
Ankit Gupta
Numerade Educator
01:40

Problem 16

Sketch the graph of the function defined by the given equation.
$G(x)=\frac{1}{2}\left(x^3-x\right)$

Dushyant Barot
Dushyant Barot
Numerade Educator
03:27

Problem 17

Sketch the graph of the function defined by the given equation.
$f(x)=x^3-2 x^2-5 x+6$

Joseph Liao
Joseph Liao
Numerade Educator
01:48

Problem 18

Sketch the graph of the function defined by the given equation.
$h(x)=x^3-3 x^2-x+3$

AG
Ankit Gupta
Numerade Educator
02:03

Problem 19

Sketch the graph of the function defined by the given equation.
$f(x)=x^4$

Eric Mockensturm
Eric Mockensturm
Numerade Educator
00:39

Problem 20

Sketch the graph of the function defined by the given equation.
$F(x)=-\frac{1}{4} x^4$

James Kiss
James Kiss
Numerade Educator
02:21

Problem 21

Sketch the graph of the function defined by the given equation.
$f(x)=x^4-x^3-2 x^2+3 x-3$

Joseph Liao
Joseph Liao
Numerade Educator
01:14

Problem 22

Sketch the graph of the function defined by the given equation.
$g(x)=x-x^4$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:29

Problem 23

Sketch the graph of the function defined by the given equation.
$f(x)=(x-1)^2(x-2)$

James Kiss
James Kiss
Numerade Educator
01:20

Problem 24

Sketch the graph of the function defined by the given equation.
$g(x)=(x-1)\left(4-x^2\right)$

James Kiss
James Kiss
Numerade Educator
05:05

Problem 25

Sketch the graph of the function defined by the given equation.
$f(x)=x(1-x)^3$

Eric Mockensturm
Eric Mockensturm
Numerade Educator
01:29

Problem 26

Sketch the graph of the function defined by the given equation.
$g(x)=\left(x^2-1\right)(x-2)^2$

James Kiss
James Kiss
Numerade Educator
02:17

Problem 27

Show that the graph of $y=a x^4+b x^2+c$ has the property that if it contains the point $\left(x_1, y_1\right)$, then it also contains the point $\left(-x_1, y_1\right)$. Any function whose graph has this property is called an even function. Notice that the graph of an even function is symmetric with respect to the $y$-axis.

Abigail Martyr
Abigail Martyr
Numerade Educator
01:37

Problem 28

Show that the graph of $y=a x^5+c x^3+e x$ has the property that if it contains the point $\left(x_1, y_1\right)$, then it also contains $\left(-x_1,-y_1\right)$. Any function whose graph has this property is called an odd function. An odd function is sometimes said to be symmetric with respect to the origin.

Carson Merrill
Carson Merrill
Numerade Educator