Question

question
determine whether ( y = -2x^2 - 3 ) is a function.
select the correct answer below:
( circ ) yes
( circ ) no

Explanation:

Step1: Recall the definition of a function

A relation is a function if for every input \( x \) (in the domain), there is exactly one output \( y \). For the equation \( y = -2x^2 - 3 \), we can analyze the mapping from \( x \) to \( y \).

Step2: Analyze the given equation

For any real number \( x \) we substitute into the equation \( y=-2x^{2}-3 \), we will get exactly one value of \( y \). For example, if \( x = 0 \), then \( y=-2(0)^{2}-3=- 3 \); if \( x = 1 \), then \( y=-2(1)^{2}-3=-2 - 3=-5 \); if \( x=- 1 \), then \( y=-2(-1)^{2}-3=-2 - 3=-5 \). Even though different \( x \)-values (like \( x = 1 \) and \( x=-1 \)) can give the same \( y \)-value, the key is that each \( x \) gives only one \( y \). This equation represents a parabola that opens downward, and it passes the vertical line test (if we draw a vertical line anywhere on the graph of the equation, it will intersect the graph at most once).

Answer:

yes