
Math 3 Semester 1 Review (Unit 1)
Presentation
•
Mathematics
•
11th Grade
•
Medium
+4
Standards-aligned
Gema Venegas
Used 1+ times
FREE Resource
12 Slides • 20 Questions
1
Unit 1: Polynomials
2
Polynomial End Behavior
3
Multiple Choice
What is the end behavior of the polynomial?
As x→−∞, f(x)→+∞ As x→+∞, f(x)→−∞
As x→−∞, f(x)→+∞ As x→+∞, f(x)→+∞
As x→−∞, f(x)→−∞ As x→+∞, f(x)→−∞
4
Multiple Choice
What is the end behavior of the polynomial?
As x→−∞, f(x)→−∞ As x→+∞, f(x)→+∞
As x→−∞, f(x)→+∞ As x→+∞, f(x)→+∞
As x→−∞, f(x)→−∞ As x→+∞, f(x)→−∞
5
Polynomial End Behavior
The degree and leading coefficient of a polynomial can help us find the end behavior of a polynomial's graph.
6
Polynomials
7
Multiple Choice
What is the end behavior of the polynomial below? (Hint: Look at the degre and leading coefficient)
f(x)=−2x3+4x2−9x+1
As x→−∞, f(x)→−∞ As x→+∞, f(x)→+∞
As x→−∞, f(x)→+∞ As x→+∞, f(x)→+∞
As x→−∞, f(x)→+∞ As x→+∞, f(x)→−∞
8
Domain and Range
9
Multiple Choice
What is the domain of this function?
−1≤x≤3
x<−3
−1≤x≤2
all real numbers
10
Multiple Choice
What is the range?
all real numbers
y≥−1
−1≤y≤3
y≥3
11
Multiple Choice
What is the range?
all real numbers
y≥0
0<y<5
y≥−1
12
An Absolute Max is the highest point on the graph.
Absolute Max and Min
An Absolute Min is the lowest point on the graph.
13
A relative max is a peak on the graph.
A relative min is a pit on the graph.
Relative Max and Min
14
Labelling
Label the following points on the graph.
Absolute Min
Absolute Max
Relative Min
15
Multiple Choice
The blue dot on this graph represents a(n)...
Absolute Maximum
Absolute Minimum
Relative Maximum
Relative Minimum
16
Multiple Choice
The point (1, 4) is a(n)...
Absolute Maximum
Absolute Minimum
Relative Maximum
Relative Minimum
17
Multiple Select
Which interval(s) is the function increasing on?
Select 2 answers.
−2<x<2
x<−1
x>1
−1<x<1
18
Multiple Choice
Which interval is the function decreasing on?
−2<x<2
x<−1
x>1
−1<x<1
19
A root or zero, is where the polynomial is equal to zero.
We can find the zeros of a polynomial from its graph by looking at the x -intercepts.
Zeros of Polynomials
20
Multiple Choice
What are the "zeros" of this polynomial?
-2, -1
-2, -1, 0, 1, 2
-2, -1, 1, 2
-2, -1, 4, 1, 2
21
The zeros of a polynomial have different multiplicities depending on what they look like as they cross the x - axis.
This is helpful for when we are writing the equation of a polynomial in factored form.
Multiplicities of Zeros
22
Multiple Choice
Identify a possible equation for the polynomial.
f(x)=(x+3)(x+1)(x+5)
f(x)=(x−3)(x−1)(x−5)
f(x)=(x−3)(x−1)(x+5)
f(x)=(x+3)(x+1)(x−5)
23
Multiple Choice
Add the polynomials.
(9x3+5x2−3x)+(4x3−8x2+7x)
13x3−3x2−4x
13x3−13x2+4x
13x3−3x2+4x
14x6
24
Multiple Choice
Subtract the polynomials.
(4x3−3x2+6x−4)−(−2x3+x2−20)
4x2−6x3−2x+6
3x+5x2+1
6x2−4x2+6x+16
3x+2
25
Multiple Select
Multiply
(4x+3)(2x−1)
8x2−2x−3
8x2−3
8x2+6x−3
8x2+2x−3
26
Multiple Select
Multiply
(4x+3)(2x−1)
8x2−2x−3
8x2−3
8x2+6x−3
8x2+2x−3
27
Watch the video below for a review on how to divide Polynomials using Synthetic Division.
28
Multiple Choice
Cam divided (x4 + 3x2 - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?
Cam wrote the remainder incorrectly.
Cam did not use a zero place holder for the x3 term.
Cam added instead of subtracting the rows.
Cam should have used -2 as his division since the factor was x-2.
29
If you divide a polynomial by a linear binomial (x- r) and the remainder is zero, then the binomial is a factor.
Factor Theorem
30
Multiple Choice
(2x5+5x4−14x3+17x2−7x−3)÷(x−1) Is x-1 a factor of the polynomial?
Yes
No
31
Explanation Slide...
Yes, x-1 is a factor of the polynomial because when the polynomial is divided by x-1, the remainder is 0.
32
Multiple Choice
Is (x+2) a factor of 2x3+5x2+9 ?
yes
no
Unit 1: Polynomials
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