Question

Graph the given relation or equation and find the domain and range. Then determine whether the relation or equation is a function.
y=3x+1

Answer 1

Answer:

The equation $y = 3x +1$ is a function, for each value of x, corresponds a y-value. The domain and the range is for all the real numbers.

Step-by-step explanation:

To sketch the graph you need to make a table, propose different values of x, including negative and positives. You can see that for any value of x, you will have any value of y.

For example:

x y

-20 -59

-15 -44

-10 -29

-5 -14

0 1

5 16

10 31

15 46

20 61

Remember the following concepts:

The domain of a function f (x) is the set of all the values for which the function is defined. In other words is the collection of all possible inputs that can be plugged into a function to produce a y-value. To find the domain depends of the function type. For example a polynomial function without radicals or variables in the denominator will have all the real numbers in its domain. Usually we have to avoid 0 on the bottom of a fraction, or negative values under the square root sign.

The range of the function is the set of all the values that y takes, it is the collection of all possible outputs, depending of the function can have a minimum y-value or a maximum y-value.

We can see that the function y = 3x +1, or f(x) = 3x +1, has no restrictions, therefore the domain is all real numbers. From the graph we can see easily that y can be positive or negative. So the domain and the range can be expressed as (-∞, ∞) .

You can see the graph in the attached file.

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