2. What is the domain of y = x ^ 2 + 3x + 2
Answers
D: {x € R}
R: {y Ry - 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 € R} (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.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 € R} (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: {ye Ry - 1.25}.