Understanding Functions from Graphs

The video tutorial explores whether a set of points on a graph represents a function. It explains that for a graph to represent a function, each input must map to exactly one output. The tutorial examines specific points, showing consistent mappings for some inputs, but identifies a case where an input maps to multiple outputs, concluding that the graph does not represent a function.

What is the key requirement for a set of points to represent a function?

• Each input must have a unique output.

• Inputs and outputs must be equal.

• Each output must have a unique input.

• There must be more outputs than inputs.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What does the point (-1, 3) indicate in terms of function mapping?

• Input 3 maps to output -1.

• Input -1 maps to output 3.

• Input -1 maps to output -3.

• Input 3 maps to output 1.

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CCSS.HSF.IF.A.2

If x is 2, what is the corresponding output value according to the graph?

• -3

• 3

• 2

• -2

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What does the point (3, 2) suggest about the function?

• Input 2 maps to output -3.

• Input 3 maps to output -2.

• Input 2 maps to output 3.

• Input 3 maps to output 2.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What issue arises when inputting 4 into the function?

• 4 maps to both 1 and -1.

• 4 maps to both 2 and -2.

• 4 maps to both 3 and 2.

• 4 maps to both 5 and -1.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What does the point (4, 5) indicate in terms of function mapping?

• Input 4 maps to output -5.

• Input 5 maps to output -4.

• Input 4 maps to output 5.

• Input 5 maps to output 4.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

What does the point (4, -1) indicate in terms of function mapping?

• Input 4 maps to output -1.

• Input -1 maps to output 4.

• Input 4 maps to output 1.

• Input 1 maps to output -4.

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CCSS.8.F.A.1

Why can't the set of points be considered a function?

• Because all inputs map to the same output.

• Because one input maps to multiple outputs.

• Because there are more inputs than outputs.

• Because the graph is not linear.

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CCSS.8.F.A.1

What is a simple test to determine if a set of points is a function?

• Check if the graph is a circle.

• Check if each output has only one input.

• Check if each input has only one output.

• Check if the graph is a straight line.

What is the conclusion about the set of points on the graph?

• They represent a quadratic function.

• They represent a linear function.

• They represent a constant function.

• They do not represent a function.