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Example Questions
Example Question #1 :Graphs Of Inverse Trigonometric Functions
True or False: The inverse of the functionis also a function.
True
False
False
Consider the graph of the function. It passes the vertical line test, that is if a vertical line is drawn anywhere on the graph it only passes through a single point of the function. This means thatis a function.
Now, for its inverse to also be a function it must pass the horizontal line test. This means that if a horizontal line is drawn anywhere on the graph it will only pass through one point.
This is not true, and we can also see that if we graph the inverse of() that this does not pass the vertical line test and therefore is not a function. If you wish to graph the inverse of, then you must restrict the domain so that your graph will pass the vertical line test.
Example Question #1 :Graphs Of Inverse Trigonometric Functions
Which of the following is the graph of the inverse ofwith?
Note that the inverse ofis not, that is the reciprocal. The inverse ofisalso written as. The graph ofwithis as follows.
And so the inverse of this graph must be the following withand
Example Question #3 :Graphs Of Inverse Trigonometric Functions
Which best describes the easiest method to graph an inverse trigonometric function (or any function) based on the parent function?
Theandvalues are switched so wherefor the parent function,for the inverse function.
Thevalues are swapped withso wherefor the parent function,for the inverse function.
Letso wherefor the parent functionfor the inverse function.
Letso wherefor the parent function,for the inverse function.
Example Question #4 :Graphs Of Inverse Trigonometric Functions
Which of the following represents the graph ofwith?
If we are looking for the graph ofwith, that means this is the inverse ofwith. The graph ofwithis
Switching theandvalues to graph the inverse we get the graph
Example Question #1 :Graphs Of Inverse Trigonometric Functions
Which of the following is the graph ofwith?
We first need to think about the graph of the function.
Using the formulawhereis the vertical shift, we have to perform a transformation of moving the functionup two units on the graph.
Example Question #92 :Trigonometric Functions And Graphs
下面哪个选项是正确的图和类风湿性关节炎nge of the inverse function ofwith?
First, we must solve for the inverse of
So now we are trying to find the range of and plot the function. Let’s start with the graph of. We know the domain is.
Now using the formulawhere= Period, the period ofis. And so we perform a transformation to the graph ofto change the period fromto.
We can see that the graph has a range of
Example Question #93 :Trigonometric Functions And Graphs
True or False: The domain forwill always be all real numbers no matter the value ofor any transformations applied to the tangent function.
False
True
Example Question #94 :Trigonometric Functions And Graphs
Which of the following is the graph of?
First, we must consider the graph of.
Using the formulawe can apply the transformations step-by-step. First we will transform the amplitude, soso we must shorten the amplitude to.
Now we must apply a vertical shift of one unit since. This leaves us with our answer.
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