Pre Calc Unit 1 Review

Front

What does it mean for a function to be always increasing?

Back

A function is always increasing if, for any two points x1 and x2 in its domain, if x1 < x2 then f(x1) < f(x2). This means that as the input values increase, the output values also increase.

Front

What is the definition of inverse functions?

Back

Inverse functions are two functions that 'undo' each other. If f(x) is a function, then its inverse f^(-1)(x) satisfies the condition f(f^(-1)(x)) = x for all x in the domain of f^(-1).

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, then the graph does not represent a function.

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 the points (1,3), (2,4), (6,8) is (3,1), (4,2), (8,6).

Front

What is the significance of f(0) in a function?

Back

f(0) represents the value of the function when the input is zero. It is often referred to as the y-intercept of the function when graphed.

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean for two functions to be inverses of each other?

Back

Two functions are inverses if applying one function to the result of the other function returns the original input. This means f(f^(-1)(x)) = x and f^(-1)(f(x)) = x.

Front

What is the domain of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that the function can produce.

Front

What is a one-to-one function?

Back

A one-to-one function is a function in which each output value is associated with exactly one input value. This means that no two different inputs produce the same output.