Foreword
Determined Parameters value range, is very popular in high school math class a title, is now used to summarize finishing. ,
Domain range
- Known domain or range, parameter ranges required
① If the domain of the function is \ (R & lt \) , the unknown parameters \ (A \) ranges;
Preparatory: Think first, the domain of this function should be how to solve?
Analysis: Since the domain of the function is \ (R & lt \) , explanation for any \ (X \ in R & lt \) , that can \ (G (X) = X ^ 2 + 2AX-A> 0 \) ,
Converted to a quadratic function established constant problem, (at this time or at least can be considered constant established Shuoxingjiege separation parameter)
Shuoxingjiege used here, the function \ (g (x) \) opens upward, and \ (X \) axis there is no intersection, then \ (\ of Delta <0 \) ,
I.e., \ (\ of Delta = (. 2A) ^ 2-4 \ Times. 1 \ Times (-a) <0 \) , solve for \ (A \ in (-1,0) \) .
② If the range is a function \ (R & lt \) , the unknown parameters \ (A \) ranges;
Analysis: As shown on the right, so that the function to \ (f (x) \) the range is \ (R & lt \) , described the function \ (g (x) = x ^ 2 + 2ax-a \) must be You can take over all positive numbers, in conjunction with the FIG.,
If there is a positive real number does not take part to, then the function \ (f (x) \) of the range would not be \ (R & lt \) , so that only a function \ (g (x) \) a \ (\ of Delta \ GE 0 \) ,
But can not be \ (\ of Delta <0 \) , attention is now subject of the request range of \ (R & lt \) , rather than the domain of \ (R & lt \) ,
Must satisfy the condition \ (\ of Delta = (. 2A) ^ 2-4 \ Times. 1 \ Times (-a) \ GE 0 \) , solve for \ (a \ in \ {a \ mid a \ leq -1, a \ GE 0 \} \) .
FIG next parameter \ (a \ in [-3,3] \) dynamic changes image when the two functions;
FIG next parameter \ (a \ in (-1,0) \) dynamic changes image when the two functions;
