Inverse Functions and Graphing

The video tutorial explains how to find the inverse of a function, using f(x) = -x + 4 as an example. It demonstrates the algebraic steps to solve for the inverse, graphing the inverse function, and understanding the concept of function mapping. The tutorial also includes a second example with g(x) = -2x - 1, showing how to find and graph its inverse. The key takeaway is that a function and its inverse are reflections over the line y = x.

What is the first step in finding the inverse of a function?

• Find the y-intercept

• Graph the function

• Solve for y in terms of x

• Solve for x in terms of y

When graphing the inverse of f(x) = -x + 4, what do you notice about the graph?

• It is a parabola

• It is a horizontal line

• It is a vertical line

• It overlaps with the original function

What happens to the graph of a function when it is its own inverse?

• It overlaps with the line y = x

• It reflects over the y-axis

• It becomes a circle

• It shifts upwards

What is the relationship between a function and its inverse on a graph?

• They are parallel

• They are perpendicular

• They are reflections over the line y = x

• They intersect at the origin

If f(5) = -1, what is f inverse of -1?

• -1

• 1

• -5

• 5

In the context of inverse functions, what does it mean for a function to map from one value to another?

• It changes the y-intercept

• It reflects over the x-axis

• It changes the slope

• It transforms the input to the output

In the example with g(x) = -2x - 1, what is the y-intercept of the inverse function?

• 1/2

• -1

• 0

• -1/2

What is the slope of the inverse function of g(x) = -2x - 1?

• -1/2

• -2

• 1/2

• 2

How do you express the inverse function as a function of x?

• By solving for y in terms of x

• By finding the slope

• By renaming y as x

• By graphing the function

What is the general process to find the inverse of a function?

• Solve for y, then graph

• Solve for x, then rename y as x

• Find the slope, then solve for y

• Graph the function, then find the y-intercept