Exercise 4 Page 128

The arrows on the graph indicate that the function will continue on forever in the downward direction. This also tells us that there are no gaps in the function, and that we can input any real number for $x .$

Therefore, we can write our domain as an interval that contains all real numbers.

Domain : - \infty < x < \infty

The corresponding

y -

coordinates, on the other hand, have an upper bound at

3

because the graph does not exist above this point on the

y -

axis. Therefore, the range of the function is all possible

y -

values less than or equal to

3 .

Range : y \leq 3

Extra

More About This Function

The given function is a special type of function called a quadratic. The parent function of a quadratic function is $y = x^{2} .$

Unless there are specific restrictions mentioned, the domain of a quadratic function is always going to be all real numbers. The range of an unrestricted quadratic function will always be from the point where the direction changes, which is called the vertex, to either infinity or negative infinity depending on if it opens up or down.

You will learn more about this type of function later in this course!