Inverses
State the inverse relation:
(-3, 9), (-2, 4), (-1,1), (0,0), (1, 1), (2, 4)
(9, -3), (4, -2), (1, -1), (0, 0), (1, 1), (4, 2)
Identify the degree and leading coefficient.
-2x2 - 7x + 9x4 - 3
Degree: 4
Leading coefficient: 9
Describe the end behavior of
f(x) = -x2 - 3x +1
Left and right fall
What is the parent function in
f(x) = 5(x - 2)3 - 11?
Cubic or f(x) = x3
We can use this test to determine if a function is one to one
Horizontal Line Test
Find the inverse:
f(x) = 5x + 9
f-1 (x) = (x - 9)/5
What is the leading coefficient?
-10x2 - 9x + 3 - 14x5
-14
Determine if the function has an odd or even degree
1. Leading coefficent is negative
2. Left side rises
3. Right side falls
Odd
Describe the transformation
g(x) = 3x3 - 9
Down 6
Vertical stretch by a factor of 3
This is the type of shift the graph makes when f(x) is changed to f(x + k), where k is a real number
Horizontal shift
Find the inverse
y = (-3/4)x + 5
y = (-4/3)x + (20/3)
Review: Classify the following polynomial by degree and number of terms
p(x) = 12x4 - 3x - 2
Quartic trinomial or 4th degree polynomial
Determine if the leading coefficient is positive or negative given that:
1. Left side falls,
2. Right side rises
Positive
Identify the parent function and Describe the transformation
f(x) = (x + 8)2 - 6
Quadratic
Left shift 8 units
Down 6
What is classroom rule number 6?
No horseplay or grooming.
Verify if the following are inverses
y= -3x - 9
y = -3x + 9
NO
Write a function that has a leading coefficient of -15 and a degree of 7
Answers will vary
Write an equation that satifies the following requirement for end behavior
1. Right side rises,
2. Left side falls,
3. Is a trinomial
Answers will vary
Must inclue
a positive coefficient, an odd degree, and three terms
What is the equation of the transformed function f(x)
absolute value- vertical shift down 3, horizontal shift 5 to the left.
f(x) = |x + 5 |- 3
Write the parent function's equation.
1. Quadratic
2. Linear
3. Square root
4. Cubic
5. Absolute value
1. f(x) = x2
2. f(x) = x
3. f(x) = Square root(x)
4. f(x) = x3
5. f(x) = |x|
Find the inverse
f(x) = (8x + 5)/4
f-1(x) = (4x - 5)/8
State the degree, leading coefficent and end behavior
f(x) = 3x3(x +2) + 4x2 - 5x
Degree 4
LC 3
Both sides up
Write three functions that have and end behavior of
left side falls
right side falls
Answers will vary.
Must include even degree and negative leading coefficient.
What is the effect on the graph of the function y= x2 + 2 when it is changed to y = x2 - 3?
It shifts down 5 units.
When is the last day of school?
May 24th