Graph of functions Practice Questions - NDA Mathematics Question Bank

Question 1 of 1 NDA MCQ

The value of ordinate of the graph of y = 2 + cos x lies in the interval

Detailed Explanation

Solution

Option (d) is correct.

Explanation:

The equation of the function is given by:

\[ y = 2 + \cos x \]

The range of \(\cos x\) is \([-1, 1]\). Thus, substituting this into the function, we have: \begin{aligned} y_{\text{min}} &= 2 + (-1) = 1 \\ y_{\text{max}} &= 2 + (1) = 3 \end{aligned} Therefore, the range of \(y\) is:

\[ [1, 3] \]

So, the ordinate of the graph, \(y\), lies in the interval \([1, 3]\).

📌 Hints / Properties Used:

Range of \(\cos x\) is \([-1, 1]\).
function transformation: \(y = f(x) + c\) shifts the graph vertically by \(c\).

📊 Visual Diagram Suggestion:

Graph of \(y = 2 + \cos x\) with indicated minimum point at \(y=1\) and maximum point at \(y=3\) on a Cartesian plane.

📖 Factual Verification & Reference:

Verified against NCERT Class XII Mathematics, Chapter 3 (Trigonometric Functions)

Graph of functions

Solution

Unlock 10,000+ Practice Questions