Relations and functions

Identify the graphs that could represent a function.

TOP: 7. 8. 9

BOTTOM: 10. 11. 12

Explain how you know if it's a function or not.

Describe the vertical line test in your own words.

​I can determine if a relation is a function using an input output mapping.

Is the relation represented by the input-output mapping a function?

• Yes

• No

Answer explanation

Yes, the relation is a function because it passes the vertical line test, meaning each input has only one corresponding output.

• Yes

• No

Answer explanation

The given relation is a function because each input value has a unique output value.

• 3

Answer explanation

The correct output values for the function are 3 and 7/3. The function evaluates to 3 when x is 1, and it evaluates to 7/3 when x is 3.

What is the definition of function?

• Has inputs and outputs

• Every input has only ONE output

• Inputs have different outputs every time

• x-values and y-values

Answer explanation

A function is a mathematical relationship where every input has only one output.

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.

• Yes, because each x-value has only one y-value paired with it.

• No, because the x-value 11 has two y-values pair with it.

• No, because each x-value has only one y-value paired with it.

Answer explanation

No, because the x-value 11 has two y-values paired with it. Each x-value should have only one y-value paired with it.

What is the Domain and range for the graph in interval notation?

• D: y=0

  R: (0, 1)

Answer explanation

The domain is all real numbers, and the range is all positive numbers. The correct choice is D: (-∞, ∞) for the domain and R: (0, ∞) for the range.

What is my first step to find the discontinuities for this function?

• Factor the numerator and denominator

• Plug in zero

• Cancel the x² on the numerator and denominator

Answer explanation

To find the discontinuities, factor the numerator and denominator.

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.

• Yes, because each x-value has only one y-value paired with it.

• No, because the x-value 11 has two y-values pair with it.

• No, because each x-value has only one y-value paired with it.

Answer explanation

No, because the x-value 11 has two y-values paired with it.