The graphs and whether they represent a function or not go like this:
Graph 1: No, Graph 2: No, Graph 3: Yes, Graph 4: Yes, Graph 5: Yes, Graph 6: Yes
What is a function?
A function is a relation between a dependent variable (say y ) and an expression of an independent variable (say x), used to determine the value of a dependent variable from a given value of an independent variable.
When is a relation called a function?
For a relation to be known as a function, there should be one and only one value of y to a value of x and not more.
How do we solve the given question?
We are asked to say whether the given graphs represent a function or not. We check each graph at a time.
- Graph 1: Not a function as one value of x has more than one value of y, for example, x = 0 gives y = 1 and -1.
- Graph 2: Not a function as one value of x has more than one value of y, for example, x = 0 gives y = 3 and -3.
- Graph 3: Is a function as no value of x gives more than one value for y.
- Graph 4: Is a function as no value of x gives more than one value for y.
- Graph 5: Is a function as no value of x gives more than one value for y.
- Graph 6: Not a function as one value of x has more than one value of y, for example, x = -2 gives y = 2 and 3.
∴ We can choose options like this:
Graph 1: No, Graph 2: No, Graph 3: Yes, Graph 4: Yes, Graph 5: Yes, Graph 6: Yes.
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