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A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

$ f(t) $ is your height at age $ t $.

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It is not a $1-$ to- $-1$ function.

01:15

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Johns Hopkins University

Missouri State University

Campbell University

Boston College

Lectures

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A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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okay to figure out if this is a 1 to 1 function. Let's make a rough sketch of your height at various ages in your life. So let's assume that you grew for a certain amount of time and then perhaps your height stayed the same. And maybe at the end of your life, it went down well. If this is 1 to 1, then for every X value there's only one y value. And for every y value, there's only one X value, so it must pass the vertical line test and the horizontal line test. Since it's a function, it passes the vertical line test for every X value. There's only one y value, but it fails the horizontal line test because there are plenty of years in your life when you were the exact same height. So that's a fail. So no, this is not a 1 to 1 function

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