Math 3 Exam Review Unit 1

Front

What are inverse functions?

Back

Inverse functions are functions that reverse the effect of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y and produces the original input x.

Front

How do you determine if two functions are inverses of each other?

Back

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you find the inverse of a set of points?

Back

To find the inverse of a set of points, switch the x and y coordinates of each point. For example, the inverse of (1,3) is (3,1).

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f⁻¹(x), where f is the original function.

Front

What is the significance of the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one (and thus has an inverse). If any horizontal line intersects the graph of the function more than once, the function does not have an inverse.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements. This means that each output is produced by exactly one input.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function g at a specific point, substitute the value into the function. For example, g(4) means to replace x with 4 in the function g.

Front

What is the process for finding the inverse of a function algebraically?

Back

To find the inverse of a function algebraically, replace f(x) with y, swap x and y, and then solve for y. The resulting equation is the inverse function.