Identify the type of function represented by the equation y = – 3.
a
absolute value
b
quadratic
c
constant
The Correct Answer and Explanation is :
The equation ( y = -3 ) represents a constant function (option c).
Explanation:
A constant function is defined as a function that assigns the same value to every input in its domain. In the case of the equation ( y = -3 ), regardless of the value of ( x ), the output ( y ) remains (-3). This means that for any input, whether ( x = 0, 1, -5, ) or any other number, the output will always be (-3).
To visualize this, if you were to graph the function ( y = -3 ), you would plot a horizontal line that intersects the y-axis at (-3). This horizontal line extends infinitely in both the left and right directions on the x-axis, indicating that all x-values correspond to the same y-value of (-3).
Characteristics of Constant Functions:
- Graph: The graph of a constant function is a horizontal line. For ( y = -3 ), this line is parallel to the x-axis.
- Slope: The slope of a constant function is zero because there is no change in ( y ) as ( x ) changes. The rate of change of the function is always ( 0 ).
- Domain and Range: The domain of the function ( y = -3 ) is all real numbers ((-\infty, \infty)), while the range is limited to the single value (-3).
- Equation Form: Constant functions can generally be expressed in the form ( y = c ), where ( c ) is a constant value. In this case, (-3) is the constant value.
In contrast, an absolute value function typically has a V-shape graph that opens upward or downward depending on its transformations. A quadratic function is represented by a parabolic graph and generally has a variable ( x^2 ) term, which leads to curvature in its graph. Thus, ( y = -3 ) does not fit these categories, reaffirming that it is indeed a constant function.