Parent Functions & Transformations
Linear Functions
Absolute Value Inequalities
Absolute Value Functions
Trivia
100
What is a parent function?
The original function (most basic form).
100
What is the equation of a line?
y = mx + b
100
What is the difference between open circle and close circle for the solutions of an inequality?
Open circle means the number is not a solution
Close circle means the number is a solution
or
Open = not included
Close = included
100
What is the parent function to all absolute value functions?
f(x) = |x|
100
What percentage of the original four Teenage Mutant Ninja Turtles have names ending with the letter o?
75% (Leonardo, Donatello, Michelangelo, Raphael)
200
What is the parent function of:
g(x) = 2x2+3
Quadratic
200
What is the domain and range?
Domain: All real numbers
Range: All real numbers
200
Is -4 a solution to the following inequality:
|2x+7| > 1
not a solution
200
Identify and describe the transformation:
g(x) = |x| + 4
Vertical translation of four up
200
Thanks to the magic of mathematical predictions, what planet was accurately postulated in 1846…before it was observed?
Neptune
300
Which of the following functions have the same parent function?
a. y = 2x + 3 and y = 0.5x -7
b. y = 2x3-1 and y = x2+14
c. y = |x+4| and y = (x-3)3
d. y = 4/x and y = 17.5x + 3
a. y = 2x + 3 and y = 0.5x -7
300
What is the y and x-intercept?
y-int: (0,2)
x-int: (-1,0)
300
Solve the following inequality:
|x+4| < 2
x < -2 and x > -6
300
Describe the transformation:
Left 4 and up 3
300
Who is nicknamed "The Father of Geometry"?
Euclid
400
Identify the parent function and describe the transformation.
g(x) = x+4
Parent Function: Linear
Transformation: translation up 4 or translation left 4
400
What is the equation of the line:
y = 2x + 2
400
Solve and graph the inequality:
4|2x-1|-2 > 10
x > 2 or x < -1
400
Identify and describe the transformation:
h(x) = 0.5|x-3| + 1
Vertical shrink by 0.5
Right 3 and up 1
400
Subtract the number of states that border Mexico from the number of states that border Canada, and you get what?
Seven (11–4)
500
Identify the parent function and describe the transformation.
h(x) = (x-1)2+3
Parent: Quadratic
Transformation: Right 1, up 3
500
What is the equation of the line given the points:
(3,4) and (2,1)
y = 3x - 5
500
Solve and graph the inequality:
-2|x+1| > 3
No solution
500
Describe the transformation:
Reflection across x-axis
Right 2
Down 1
Vertical compression 2
500
What’s more: the number of feet in a mile, or the number of pounds in two tons?
Feet in a mile (5,280 vs. 4,000)