GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsHard
A meteorologist is tracking the temperature in a desert region. The temperature, T, in degrees Celsius, at different times of the day, t (in hours from midnight), is recorded as a set of points. Which of the following sets of points represents a function?
- A{(7, 28), (9, 32), (11, 36), (13, 32)}
- B{(5, 20), (5, 22), (7, 24), (9, 26)}
- C{(6, 25), (8, 30), (8, 35), (10, 38)}
- D{(12, 40), (12, 42), (14, 45), (16, 48)}
Show answer & explanationAnswer & explanation
Correct answer: A. {(7, 28), (9, 32), (11, 36), (13, 32)}
A set of points represents a function if each input (x-value) corresponds to exactly one output (y-value). In option B, each time (t-value) has only one recorded temperature (T-value). Options A, C, and D all have at least one input value (time) with multiple output values (temperatures), which violates the definition of a function.
Why the other options are wrong
- B. This is incorrect because the input '5' is paired with two different outputs ('20' and '22').
- C. This is incorrect because the input '8' is paired with two different outputs ('30' and '35').
- D. This is incorrect because the input '12' is paired with two different outputs ('40' and '42').
Definition of a Function
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
- Each x-value (input) must have only one y-value (output).
- It can be represented as a set of ordered pairs, a graph, or an equation.
- The vertical line test can be used to determine if a graph represents a function.
Memory trick: One Input, One Output; No Cheating!