Horizontal Line Test

Author:: mathtasksproj, Carlos

We say

is a 1 to 1 function if whenever

and

we have

. The mathematical term 'injective' is also used for these functions. We say

is an onto function if the range of

is equal to

. The mathematical term 'surjective' is also used for these functions. On the following graph, adjust the values of

to move the line

and find points of intersection between the line and the function

Graph of f(x)

1A)

Is this function 1-1? Explain your answer.

Check my answer

2A)

Are there any intervals for which f(x) is 1-1?

Select all that apply

A
B
C
D
There are no intervals for which the function is 1-1

Check my answer (3)

3A)

Is this function onto? Explain why.

Check my answer

Now consider the function

below:

Graph of g(x)

1B)

Is this function injective? Explain your answer.

Check my answer

2B)

Are there any intervals for which f(x) is injective?

Select all that apply

A
B
C
D
There are no intervals for which the function is 1-1

Check my answer (3)

3B)

Is this function surjective? Explain why.

Check my answer

What features should a graph have in order to represent a 1-1 function? What about an onto function? Test your conjectures by entering a function in the graph below and applying the appropriate tests.

Horizontal Line Test

Graph of f(x)

1A)

2A)

3A)

Graph of g(x)

1B)

2B)

3B)

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