Question

Which relations are functions?

Select Function or Not a function for each graph.

Answer 1

Graph 1 and 2 are functions but graph 3 and 4 are not functions.

Explanation:

1. The first graph is of a straight line, which passes through the origin(0,0) and point (1,2).

Therefore, the equation of the straight line is y = mx {No y-intercept since the graph passes through origin}

Now, putting x = 1 and y = 2 we get, m = 2.

So, the equation becomes y = 2x which is a function because we will get one value of y regardless of the number of values of x.

2. This is a graph of a parabola having the vertex at (1,0) and axis parallel to the positive x-axis.

Now, the equation of the parabola is (x - 1)² = 4a(y - 0) = 4ay

Now, this graph also passes through (0,1) point.

So, (-1)² = 4a, ⇒
`a = (1)/(4)`

Therefore, the equation is (x - 1)² = y, which is a function because we will get one value of y regardless of the number of values of x.

3. This is an equation of not a function x = |y| i.e. x = y for y ≥ 0 and x = - y for y < 0 i.e. for one value of x we can have more than one output, that means more than one y values.

4. This is a equation of a circle having center at (0,0) and radius = 2.

Therefore, the equation is
`x^(2) + y^(2) = 4` which is also not a function i.e. for one value of x we can have more than one output, that means more than one y values.

Therefore, graph 1 and 2 are functions but graph 3 and 4 are not functions. (Answer)