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Example: Calculator to evaluate inverse trig function | Trigonometry | Khan Academy
By Khan Academy
Example using calculator to evaluate inverse tangent function
Understanding logarithms as inverse exponentials
By Khan Academy
Given incomplete tables of values of b^x and its corresponding inverse function, log_b(y), Sal uses the inverse relationship of the functions to fill in the missing values.
Inverse Right Triangle Trigonometry
By kthomp271828
Inverse trig functions are used to find missing angles rather than missing sides. This video explains how to use inverse trig to find a missing angle.
Inverse Functions | MathHelp.com
By MathHelp.com
In this example, we’re given a relation in the form of a chart, and we’re asked to find the inverse of the relation, then graph the relation and its inverse. To find the inverse of a relation, we simply switch the x and y values in each point. In other words, the point (1, -4) becomes (-4, 1), the point (2, 0) becomes (0, 2), the point (3, 1) becomes (1, 3), and the point (6, -1) becomes (-1, 6). Next, we’re asked to graph the relation and its inverse, so let’s first graph the relation. Notice that the relation contains the points (1, -4,), (2, 0), (3, 1), and (6, -1). And the inverse of the relation contains the points (-4, 1), (0, 2), (1, 3), and (-1, 6). Finally, it’s important to understand the following relationship between the graph of a relation and its inverse. If we draw a diagonal line through the coordinate system, which is the line that has the equation y = x, notice that the relation and its inverse are mirror images of each other in this line. In other words, the inverse of a relation is the reflection of the original relation in the line y = x.
Function inverses example 3 | Functions and their graphs | Algebra II | Khan Academy
By Khan Academy
Function Inverse Example 3: f(x)= (x - 1) squared -2 This is the last segment of Mr. Khan's short 4-part series on Function Inverses. These installments started with Khan's Introduction to Function Inverses. Mr. Khan uses the Paint Program (with different colors) to illustrate his points. Sal Khan is the recipient of the 2009 Microsoft Tech Award in Education. The screen gets busy (and dark)--the viewer may want to open to 'full screen' to see everything. The sound is a little low.
Systems of Three Equations | MathHelp.com
By MathHelp.com
Here we’re asked to graph the following function and use the horizontal line test to determine if it has an inverse. And if so, find the inverse function and graph it. So let’s start by graphing the given function, f(x) = 2x – 4, and remember that f(x) is the same as y, so we can rewrite the function as y = 2x – 4. Now, we simply graph the line y = 2x – 4, which has a y-intercept of -4, and a slope of 2, or 2/1, so we go up 2 and over 1, plot a second point and graph our line, which we’ll call f(x). Next, we’re asked to use the horizontal line test to determine if the function has an inverse. Since there’s no way to draw a horizontal line that intersects more than one point on the function, the function does have an inverse. So we need to find the inverse and graph it. To find the inverse, we switch the x and the y in original function, y = 2x – 4, to get x = 2y – 4. Next, we solve for y, so we add 4 to both sides to get x + 4 = 2y, and divide both sides by 2 to get 1/2x + 2 = y. Next, let’s flip our equation so that y is on the left side, and we have y = 1/2x + 2. Finally, we replace y with the notation that we use for the inverse function of f, as shown here. And remember that we’re asked to graph the inverse as well, so we graph y = ½ x + 2. Our y-intercept is positive 2, and our slope is ½, so we go up one and over 2, plot a second point, graph the line, and label it as the inverse function of f. Notice that the graph of the inverse function is a reflection of the original function in the line y = x.
Function inverses example 2 | Functions and their graphs | Algebra II | Khan Academy
By Khan Academy
Function Inverse Example 2: f(x)= (x + 2) squared +1 This is a another installment of Mr. Khan's short 4-part series on Function Inverses. Mr. Khan uses the Paint Program (with different colors) to illustrate his points. Sal Khan is the recipient of the 2009 Microsoft Tech Award in Education. The screen gets busy (and dark)--the viewer may want to open to 'full screen' to see everything. The sound is a little low.
Introduction to function inverses | Functions and their graphs | Algebra II | Khan Academy
By Khan Academy
Introduction to Function Inverses. Mr. Khan uses the Paint Program (with different colors) to illustrate his points. Sal Khan is the recipient of the 2009 Microsoft Tech Award in Education. The screen gets busy (and dark)--the viewer may want to open to 'full screen' to see everything. The sound is a little low.
16 - Simplify Logarithms - Part 1 (Log Bases, Calculate Logarithms & More)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
Algebra Applications: Exponential Functions
By Media4Math
In this episode of Algebra Applications, students explore earthquakes using exponential models. In particular, students analyze the earthquake that struck the Sichuan Province in China in 2008, months before the Beijing Olympics. This dramatic, real-world example allows students to apply their understanding of exponential functions and their inverses, along with data analysis and periodic function analysis. Segments include: What is an earthquake? The basic definition of an exponential function is shown in the intensity function for an earthquake. Students analyze data and perform an exponential regression based on data from the Sichuan earthquake. What is the difference between earthquake intensity and magnitude? An exponential model describes the intensity of an earthquake, while a logarithmic model describes the magnitude of an earthquake. In the process students learn about the inverse of an exponential function. How is earthquake magnitude measured? An earthquake is an example of a seismic wave. A wave can be modeled with a trigonometric function. Using the TI-Nspire, students link the amplitude to an exponential function to analyze the dramatic increase in intensity resulting from minor changes to magnitude. Go to www.media4math.com for additional resources.
12 - What are Inverse Functions? (Part 1) - Find the Inverse of a Function & Graph
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
10 - What are Composite Functions? (Part 1) - Evaluating Composition of Functions & Examples
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
15 - What is a Logarithm (Log x) Function? (Calculate Logs, Applications, Log Bases)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
11 - Learn ArcSin, ArcCos & ArcTan (Inverse Sin, Cos & Tan) - Part 1
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
18 - Properties of Logarithms (Log x) - Part 1 - Laws of Logs - Calculate Logs & Simplify
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
What is a Natural Log Ln(x)? - Part 1 (Logarithm w/ Base e - Euler's number)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!