Question

directions: select all the correct answers.
select all relations that are functions.

0	4
3	8
6	12
9	16

(-3, 3), (-1, 1), (-1, 3), (2, -2)

graph of a line on a coordinate plane

y = 2x³ + 5/4

Explanation:

To determine if a relation is a function, we use the definition: a relation is a function if every input (x - value) has exactly one output (y - value).

Step 1: Analyze the table

The table has x - values 0, 3, 6, 9. Each x - value has a unique y - value (4, 8, 12, 16 respectively). So, this relation is a function.

Step 2: Analyze the set of ordered pairs \((-3,3),(-1,1),(-1,3),(2, - 2)\)

For the x - value \(-1\), we have two different y - values (1 and 3). So, this relation is not a function.

Step 3: Analyze the graph

We can use the vertical line test. A vertical line drawn anywhere on the graph will intersect the graph at most once. So, this graph represents a function.

Step 4: Analyze the equation \(y = 2x^{3}+\frac{5}{4}\)

For any real number input \(x\), when we substitute \(x\) into the equation, we will get exactly one real number output \(y\) (since it is a polynomial function, and polynomial functions are functions). So, this relation is a function.

Answer:

The relations that are functions are:

• The table (with x - values 0, 3, 6, 9 and y - values 4, 8, 12, 16)
• The graph (the line on the coordinate plane)
• The equation \(y = 2x^{3}+\frac{5}{4}\)