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

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.