Question

The function f has a domain of {1, 3, 5, 7} and a range of {2, 4, 6}. Could f be represented by {(1, 2), (3, 4), (5, 6), (7, 2)}? Justify your answer.

Answer 1

Yes

Explanation:

- Yes, a function with those domain and range values could certainly be represented by those points.

- (1,2) and (7,2) are points with separate domain values but identical range values: this is allowed because every x value is only assigned one y value (remember, one number x in domain cannot have two different numbers y in the range).

- Another way is the use of Vertical Line test of the curve passing through to the points {(1, 2), (3, 4), (5, 6), (7, 2)}. sketch down multiple vertical lines passing through the curve. If any particular vertical line intersects the curve at more than one point on the curve then the curve is not a function of y = f(x).

- You would see that all vertical lines are free this invalidation. Hence, y is a function of x having points {(1, 2), (3, 4), (5, 6), (7, 2)}.