Lesson 4.1: Finding x-intercepts, y-intercepts, and Converting to Standard Form
Lesson 4.1b: Transformations
Lesson 4.2: Symmetry
Lesson 4.3: Even OR Odd
Lesson 4.3: Extrema
100
How do we find x-intercepts using factored form? How do we find y-intercepts using factored form?
x-intercepts: Set each factor equal to 0.
y-intercepts: Convert to standard, look for the number without a variable (d-value)
100
What do each of the values do to the function (What do A, C, and D do to the function?
T(x)=A(x-C)^3+D
A: Negative - Reflection, Whole number - Vertical Stretch, Fraction - Vertical Compression
C: x-C - Right, x+C - left
D: +D - Up, -D - Down
100
Identify if the SYMMETRY is EVEN, ODD, or NEITHER.
f(x)=x^5-3x^3+x
ODD
100
Determine the end behavior of the function:
As x approaches negative infinity, the graph ______
As x approaches POSITIVE infinity, the graph ______
f(x)=x^5+3x^2+x-9
Negative infinity: FALLS
Positive infinity: RISES
100
Determine the number of extrema for the function.
3 Extrema
200
Given the function, find the y-intercept.
g(x)=4x(x-2)(x-5)
(0,0)
200
Determine the transformations of the following function:
T(x)=-2(x+3)^3-2
Reflection
Vertical Stretch by 2
Left 3
Down 2
200
Determine if the SYMMETRY is EVEN, ODD, or NEITHER.
f(x)=5x^7-4x^4+3x^2+2
NEITHER
200
As x approaches negative infinity, the graph ________
As x approaches positive infinity, the graph _________
f(x)=-2x(x-3)(x+4)
Negative Infinity: RISES
Positive Infinity: FALLS
200
Determine the number of extrema.
2
300
Determine the product of:
f(x)=3x+6
g(x)=x^2-4x+2
3x^3-6x^2-18x+12
300
Determine the transformations from m(x) to T(x) where:
m(x)=x^3 and T(x)=-14m(x-2)+5
Reflection
Vertical Stretch by 14
Right 2
Up 5
300
Determine whether the SYMMETRY is EVEN, ODD, or NEITHER.
f(x)=x^8+x^4+10
EVEN
300
For the following graph, determine if the degree of the function is EVEN/ODD and if the leading coefficient is POSITIVE/NEGATIVE.
Odd
Positive
300
What is a possible degree of the function?
x^3
400
f(x)=3x(x-2)(x+4)
Given the function, find the x-intercepts
(0,0)
(2,0)
(-4,0)
400
Given
v(x)=x^5
is vertically compressed by 1/2, shifted right 9 and shifted down 7, write the new function.
v(x)=1/2(x-9)^5-7
400
Determine whether the SYMMETRY is EVEN, ODD, or NEITHER.
NEITHER (not symmetrical about the y-axis)
400
As x approaches negative infinity, the graph _______
As x approaches positive infinity, the graph ________
g(x)=x^2(x-2)(x+1)
Negative Infinity: RISES
Positive Infinity: RISES
400
What are ALL of the possible extrema for the function:
f(x)=x^7
6, 4, 2, 0
500
Given the function, write in standard form.
f(x)=2x(x-3)(x+4)
f(x)=2x^3+2x^2-24x
500
Given the following, write out the specific cubic function:
m(x)=x^3 and T(x)=-2m(x-3)+4
T(x)=-2(x-3)^3+4
500
Determine whether the SYMMETRY is EVEN, ODD, or NEITHER.
ODD (symmetric to the origin)
500
For the following graph, determine if the DEGREE is EVEN/ODD and if the leading coefficient is POSITIVE/NEGATIVE.
EVEN
POSITIVE
500
What could be a possible degree for the function?
x^4