Question

Which of the following cannot be the graph of a function of X?

Answer 1

Answer: Choice D

Why not? Because it fails the vertical line test. Here it is possible to draw a single straight vertical line through more than one point on the curve. That's why choice D is not a function. Choices A,B,C are functions because it's impossible to draw a single vertical line through more than two points on the curve, and therefore we can say they pass the vertical line test.

Side note: choices B and C fail the horizontal line test, so these functions are not one-to-one.

Answer 2

The option that cannot be a graph of a function of X is: Option D

How to identify a function?

A function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.” The input values make up the domain, and the output values make up the range.

Now, let us analyze each of the given graphs:

A) This is clearly a linear function as seen by the straight line.

B) This is clearly a quadratic function as seen by the parabola

C) This is clearly an absolute value function.

D) This is not a function as one input value has two different output values.