How do you find the domain and range of #y=x^2+3x+1#?

1 Answer
May 2, 2017

Answer:

#"D":{x inRR}#
#"R":{y inRR|y>=-1.25}#.

Explanation:

The domain and range are a set of all the possible values that a function can have.

Domain refers to the #x#-coordinate, and range refers to the #y#-coordinate.

For a parabola, no matter the values, the domain will always be #"D":{x inRR}# (unless context is given).

As for range, the range is dependent on the #c#-value of the equation (only in vertex form).

This is because, if the #c#-value (again, only in vertex form) is #1#, then the parabola is moved up #1# units. Meaning any value below #1# is inadmissible.

Unfortunately, in this case (standard form), the #c#-value refers to the #y#-intercept. We can convert the equation to vertex form, or we can graph it and examine the parabola. We'll do that.

graph{x^2 + 3x + 1 [-3.895, 3.9, -1.948, 1.947]}

As you can see, the domain can be any #x#-value, while the range can only be values equal to or above the vertex's #y#-coordinate, #-1.25#.

Therefore, the range is #"R":{y inRR|y>=-1.25}#.

Hope this helps :)