Question

Range of \[y = {x^2} - 5x - 2\] for \[X \in \left[ { - 3,4} \right]\] is
A) \[\left[ {\dfrac{{ - 33}}{4},22} \right]\]
B) \[\left[ {\dfrac{{ - 33}}{4}, - 8} \right]\]
C) \[\left[ { - 6,4} \right]\]
D) None of these

Answer 1

Hint:
Finding range is all about finding how a function is behaving in it’s domain or given interval. For this we analyse the function by putting values of x from the given interval.

Complete step by step solution:
Given \[y = {x^2} - 5x - 2\]
For \[x = - 3\]
\[
   \Rightarrow y = {\left( { - 3} \right)^2} - 5\left( { - 3} \right) - 2 \\
   \Rightarrow y = 9 + 15 - 2 \\
   \Rightarrow y = 22 \\
 \]
For \[x = 4\]
\[
   \Rightarrow y = {\left( 4 \right)^2} - 5\left( 4 \right) - 2 \\
   \Rightarrow y = 16 - 22 \\
   \Rightarrow y = - 6 \\
 \]
So, the range should be\[\left[ { - 6,22} \right]\].

Thus option D is correct.

Additional information:
Range of a function Y is defined as the set of all outcomes for all possible values of x.
In other words mean maximum value of Y to minimum value of Y.
Domain and range of a function is also shown on a graph where on the x-axis we plot range and on the y-axis we plot the domain of a function.
A quadratic equation is of the form \[a{x^2} + bx + c = 0\].

Note:
Many students get confused in domain and range. domain is all about what values a function can take considering we should avoid indeterminate forms. Whereas Range tells us what values a function can give.