Functions & Their Graphs - Math Analysis Finals Review

Front

What is an increasing interval of a function?

Back

An increasing interval of a function is a range of x-values where the function's output (y-values) increases as x increases.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output value is associated with exactly one input value, meaning no two different inputs produce the same output.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, switch the x and y values in the equation and solve for y.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the function's output (y-values) decreases.

Front

What is the slope of a line perpendicular to the line y = 3x - 12?

Back

The slope of a line perpendicular to y = 3x - 12 is -1/3, since perpendicular slopes are negative reciprocals.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output value for each input value.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function; if any vertical line intersects the graph more than once, it is not a function.

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 determine if a function is increasing or decreasing on an interval?

Back

To determine if a function is increasing or decreasing on an interval, analyze the sign of the derivative; if the derivative is positive, the function is increasing; if negative, it is decreasing.