How to know if a graph is one to one

Asked by admin @ 29/10/2021 in Mathematics viewed by 270 People

Select all of the following graphs which are one to one functions

Answered by admin @ 29/10/2021

Given a curve in the x-y axis.

We can determine whether the curve can be the graph of a function by the "Vertical Line Test",

and we can determine whether a function is 1-1 by the "Horizontal Line Test"

The Vertical Line Test states that a curve is the graph of a function only in every single vertical line drawn in the x-y axis, cuts the curve only ONCE:

Clearly a is not the graph of a function.

b is also not a function. The line x=-2 cuts the curve more than once.

Remark: it is highly probable that the figure is not smooth enough and the vertical line x=-2 cuts the curve only at (-2, 1)

This is because the curve is very similar to the graph of $\sqrt[3]{x}$ shifted 2 units left and 1 unit up, most probably this is what was meant

BUT we have to deal with it as it appears, as we are not given any other information!

The horizontal line test states that a function is 1-1 only if every single horizontal line drawn in the x-y-axis cuts the curve ONLY once.

Check the purple horizontal lines:

a and b are not functions, so not 1-1,

c, e and f are 1-1.

d is not 1-1, as we can see that the horizontal line we drew cut the curve more than once.

Answer:

c, e, f

How to know if a graph is one to one

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