Answer:
1. Yes
2. No
3. Yes
Explanation:
A function is a relationship with unique x-values.
Defining a Function
For a relationship to be a function, the x-values cannot repeat. This means that inputs, aka x-values, can only have one possible output value, also called y-values. For example, if inputting x = 5 resulted in both y = 3 and y = 7, then the relationship would not be a function.
However, y-values do not have to be unique. Functions can repeat y-values and still be functions.
Answers
Now, let's apply this definition to the problems above.
1. The first question gives us a table of x and y-values. From the x-values in the left column, we can see that x-values do not repeat. This means the relationship is a function.
2. The second question gives the inputs and outputs of a function. From looking at the outputs for 0, we can tell that x = 0 produces multiple outputs. This means that not all x-values are unique. Thus, the relationship is not a function.
3. The third image is a graph. At no point on the graph do x-values repeat. Each x-value has one y-value. So, the relationship is a function. Specifically, this graph represents a quadratic function.