a. graph the restricted secant function, y = 3 sec x, by restricting x to the intervals 0, π/2 and (π/2, π…

a. graph the restricted secant function, y = 3 sec x, by restricting x to the intervals 0, π/2 and (π/2, π. b. use the horizontal line test to explain why the restricted secant function has an inverse function. c. use the graph of the restricted secant function to graph y = 3 sec⁻¹x. b. choose the correct answer below. a. a horizontal line intersects the graph of y = 3 sec x more than once, so the function is not one - to - one but has an inverse function. b. a horizontal line intersects the graph of y = 3 sec x more than once, so the function is one - to - one and has an inverse function. c. no horizontal line intersects the graph of y = 3 sec x more than once, so the function is one - to - one and has an inverse function. d. no horizontal line intersects the graph of y = 3 sec x more than once, so the function is not one - to - one but does have an inverse function. c. choose the correct graph below.

a. graph the restricted secant function, y = 3 sec x, by restricting x to the intervals 0, π/2 and (π/2, π. b. use the horizontal line test to explain why the restricted secant function has an inverse function. c. use the graph of the restricted secant function to graph y = 3 sec⁻¹x. b. choose the correct answer below. a. a horizontal line intersects the graph of y = 3 sec x more than once, so the function is not one - to - one but has an inverse function. b. a horizontal line intersects the graph of y = 3 sec x more than once, so the function is one - to - one and has an inverse function. c. no horizontal line intersects the graph of y = 3 sec x more than once, so the function is one - to - one and has an inverse function. d. no horizontal line intersects the graph of y = 3 sec x more than once, so the function is not one - to - one but does have an inverse function. c. choose the correct graph below.

Answer

Explanation:

Step1: Recall one - to - one function property

A function has an inverse if and only if it is one - to - one. The horizontal line test states that if no horizontal line intersects the graph of a function more than once, the function is one - to - one.

Step2: Analyze the restricted secant function

For the restricted secant function $y = 3\sec x$ with $x\in\left[0,\frac{\pi}{2}\right)\cup\left(\frac{\pi}{2},\pi\right]$, no horizontal line intersects its graph more than once. So it is one - to - one and has an inverse function.

Step3: Recall the relationship between a function and its inverse graph

The graph of $y = f^{-1}(x)$ is the reflection of the graph of $y = f(x)$ about the line $y=x$.

Answer:

b. C. No horizontal line intersects the graph of $y = 3\sec x$ more than once, so the function is one - to - one and has an inverse function. c. (Since no graphs are described in detail, we can't give a specific graph - choice answer. But in general, the graph of $y = 3\sec^{-1}x$ is the reflection of the graph of $y = 3\sec x$ (restricted as above) about the line $y = x$)