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Step-by-step explanation
To easily be able to answer these questions, you need to first understand what the terms domain and range mean.
The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists.
The range of a function refers to the region of values where the fumction can exist. It refers to the values that the dependent variable [y or f(x)] can take on.
- Starting with the first graph, we can see that for every value of x, there is a corresponding value of y, on the graph. Hence, the domain of that straight line graph is every real number. That is, x can be any real number.
On the same graph, we can see that the graph spans the whole of the y-axis, meaning that the possible values of y too and the range of this function is every real number.
- On the second graph, we can see that for every value of x, there is a corresponding value of y, on the graph. Hence, the domain of that graph is every real number.
But the graph doesn't cover the entire y-axis. It starts from y = 3 and covers the rest of any number less than y = 3. Hence, the range of this graph is all the values of y that are equal to or less than 3. That is, y ≤ 3.
- Then the third graph now. This one too has a y value for every real number value of x.
Hence, the domain of this graph too is every real number. x can be any real number.
This graph too also spans the whole of the y-axis, and the range of this function is every real number.
- On the fourth graph, we can see that this graph that looks like a quadratic graph doesn't have arrows at the end of the graph lines to indicate that the graph continues till infinity. Rather, it has an unshaded circle at the beginning at x = -3 (the unshaded sign indicates that the inequality sign is either < or >) and another shaded circle at the end of the graph at x = 3 (indicating that the inequality sign is either ≤ or ≥). Hence, the domain of this graph has to be real numbers for x that are greater than -3 but less than or equal to 3.
Domain = (-3 < x ≤ 3)
Similarly, the range of the graph will be for numbers between y = -4 and y = 4.
Range = (-4 ≤ y ≤ 4)
Hope this Helps!!!