Absolute Value Function

Bài toán Olympic 1979 Lê Bá Khánh Trình giành giải đặc biệt! IMO 1979 Problem 3
Bài toán Olympic 1979 Lê Bá Khánh Trình giành giải đặc biệt! IMO 1979 Problem 3

Equation Examples:
f(x) = |x|
f(a) = |a|
f(p) = |p|

f(x) = |x|

f(a) = |a|

f(p) = |p|

Graph, Transformations, and Inverse Examples:
f(x) = |x-1|
f(x) = 2|x-1|
f(x) = 2|x-1| – 2
f(x) = -2|x-2| + 1

f(x) = |x-1|

f(x) = 2|x-1|

f(x) = 2|x-1| – 2

f(x) = -2|x-2| + 1

*Vertex: set absolute value equal to 0, solve for x, then plug the value in the equation to find y*

Real World Situation: Barry has a bank account with a balance of $50.00. Barry owes $32.00 to his credit card company and he owes $20.00 for a yearbook. What would Barry’s bank balance be, if both debits were paid? This scenario creates a negative balance in Barry`s account of -$2.00.

Other Important Information:
– Domain: All real numbers
– Range: All points greater than or equal to the y-coordinate of the vertex (or less than or equal to, depending whether the graph opens positive or negative)
– Graph is always “V” shaped, direction of the “V” is determined by the translations
– When plugging in values to graph, one must remember that the value within the absolute value can be either positive OR negative when the absolute value has no transformations
– y intercept: when x = 0
– x intercept: when y = 0
– graphs can often not have an x or y intercept

– Domain: All real numbers

– Range: All points greater than or equal to the y-coordinate of the vertex (or less than or equal to, depending whether the graph opens positive or negative)

– Graph is always “V” shaped, direction of the “V” is determined by the translations

– When plugging in values to graph, one must remember that the value within the absolute value can be either positive OR negative when the absolute value has no transformations

– y intercept: when x = 0

– x intercept: when y = 0

– graphs can often not have an x or y intercept

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