Answer:
The range of the function is [-∞,6]
Step-by-step explanation:
Range of a Function
It's the set of values the function takes when x moves into the function's domain.
It can be graphically determined by placing imaginary horizontal lines from minus infinite to plus infinite. Where the line meets the function, that value of y belongs to the range.
The given function is:
[tex]f(x)=-x^2+6x-3[/tex]
Using a graphing tool, we draw the graph shown in the image below.
It can be clearly seen that if we imagine horizontal lines from above y=6 to infinity, they won't ever touch the graph of the function. From y=6 and below, every horizontal line will touch the function one time or twice.
We can conclude the range of the function is [-∞,6]
