Which of the following describes the graph of the function $y=2.5\sec (x-5)$?

• A. A secant graph with amplitude $2.5$, shifted left by $5$ units
• B. A cosecant graph with amplitude $2.5$, shifted right by $5$ units
• C. A secant graph with amplitude $5$, shifted right by $2.5$ units
• D. A secant graph with amplitude $2.5$, shifted right by $5$ units

Answer: (D)

Verified step by step guidance

1. Identify the given function: \(y = 2.5 \sec(x - 5)\).
2. Recall that the general form of a secant function is \(y = A \sec(B(x - C))\), where \(A\) is the amplitude (vertical stretch), and \(C\) is the horizontal shift (phase shift).
3. In the function \(y = 2.5 \sec(x - 5)\), the amplitude \(A\) is \$2.5$, indicating the graph is vertically stretched by a factor of 2.5.
4. The expression inside the secant function is \((x - 5)\), which means the graph is shifted to the right by 5 units (since \(x - C\) shifts the graph right by \(C\)).
5. Therefore, the graph is a secant graph with amplitude 2.5, shifted right by 5 units.