Question

Which of the following graphs is not a function?
a.
On a coordinate plane, a parabola opens up and goes through (negative 2, 1), has a vertex at (0, 0), and goes through (2, 1).
c.
On a coordinate, a cubic root function approaches y = negative 3 and y = 3.
b.
On a coordinate, plane a cubic root function approaches x = negative 3 and x = 3.
d.
On a coordinate plane, a parabola opens to the right and goes through (1, 1), (0, 0) and (1, negative 1).

Answer 1

d. On a coordinate plane, a parabola opens to the right and goes through (1,1);(0,0) and (1,-1).

This statement is false and thus not a function.

The equation of a parabola that passes through the points (1,1);(0.0) and (1,-1) is:

x² = 4a × y

Where, a = lenght of focii of the parabola.

The vertex of the parabola lies on (0,0).

And focii lies on (0,a)

This parabola opens upwards. And hence the statement is false.

Answer 2

The correct answer is option (d) On a coordinate plane, a parabola opens to the right and goes through (1, 1), (0, 0) and (1, negative 1).

Explanation:

• On a coordinate plane, a parabola opens to the right and goes through (1, 1), (0, 0) and (1, negative 1) is the graph which is not a function.
• The equation of this- On a coordinate plane, a parabola opens to the right and goes through (1, 1), (0, 0) and (1, negative 1) is x²= 4a.y.
• This parabola open upwards, hence the statement is false.
• In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.}
• In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.