3. y= (2x+3)(x-1)(x-4) A. leading term: B. behavior of the graph: and an_0) (nis C. x-intercepts: the polynomial in factored form is y= D. multiplicity of roots:_ E. y-intercept: F. number of turning points: G. sketch:
3. y= (2x+3)(x-1)(x-4) A. leading term: B. behavior of the graph: and an_0) (nis C. x-intercepts: the polynomial in factored form is y= D. multiplicity of roots:_ E. y-intercept: F. number of turning points: G. sketch:
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.2: Polynomial Functinos And Their Graphs
Problem 87E
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[G-ItemA] Direction: Kindly answer the given questions completely and correctly. Any missing answer will result to DISLIKING your solutions. Note: Please answer all questions.
![Graphing a Polynomial Function
To sketch the graph of a polynomial function we need to consider the following:
A. leading term
B. behavior of the graph
The graph of a polynomial function:
1. comes down from the extreme left and goes up to the extreme right if n is even and an>0.
2. comes up from the extreme left and goes up to the extreme right if n is odd and an>0.
3. comes up from the extreme left and goes down to the extreme right if n is even and an<0.
4. comes down from the extreme left and goes down to the extreme right if n is odd and an<0.
a>0
a <0
n is even
n is odd
~ ~
C. x-intercepts
D. multiplicity of roots
If r is a zero of odd multiplicity, the graph of P(x) crosses the x-axis at r.
if r is a zero of even multiplicity, the graph of P(x) is tangent to the x-axis at r.
E.y-intercept
F. number of turning points
Turning points are points where the graph from increasing to decreasing function value, or vice versa. The number of turning points
in the graph of a polynomial is strictly less than the degree of the polynomial. Also, we must note that;
1. Quartic Functions: have an odd number of turning points; at most 3 turning points
2. Quintic functions: have an even number of turning points, at most 4 turning points
3. The number of turning points is at most (n-1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff87b7007-348f-4f1b-99a4-b0bf1803e336%2Fc02ae9fe-73f1-49d5-94e8-e2e712ca277c%2Fx0vva75_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Graphing a Polynomial Function
To sketch the graph of a polynomial function we need to consider the following:
A. leading term
B. behavior of the graph
The graph of a polynomial function:
1. comes down from the extreme left and goes up to the extreme right if n is even and an>0.
2. comes up from the extreme left and goes up to the extreme right if n is odd and an>0.
3. comes up from the extreme left and goes down to the extreme right if n is even and an<0.
4. comes down from the extreme left and goes down to the extreme right if n is odd and an<0.
a>0
a <0
n is even
n is odd
~ ~
C. x-intercepts
D. multiplicity of roots
If r is a zero of odd multiplicity, the graph of P(x) crosses the x-axis at r.
if r is a zero of even multiplicity, the graph of P(x) is tangent to the x-axis at r.
E.y-intercept
F. number of turning points
Turning points are points where the graph from increasing to decreasing function value, or vice versa. The number of turning points
in the graph of a polynomial is strictly less than the degree of the polynomial. Also, we must note that;
1. Quartic Functions: have an odd number of turning points; at most 3 turning points
2. Quintic functions: have an even number of turning points, at most 4 turning points
3. The number of turning points is at most (n-1).
![3. y= (2x+3)(x-1)(x-4)
A. leading term:
B. behavior of the graph:
(nis
and an_0)
C. x-intercepts:
the polynomial in factored form is
y=.
D. multiplicity of roots:_
E. y-intercept:_
F. number of turning points:
G. sketch:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff87b7007-348f-4f1b-99a4-b0bf1803e336%2Fc02ae9fe-73f1-49d5-94e8-e2e712ca277c%2F2h0oylt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. y= (2x+3)(x-1)(x-4)
A. leading term:
B. behavior of the graph:
(nis
and an_0)
C. x-intercepts:
the polynomial in factored form is
y=.
D. multiplicity of roots:_
E. y-intercept:_
F. number of turning points:
G. sketch:
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