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Find an expression for the function whose graph is the given curve.

The line segment joining the points $ (1 , -3) $ and $ (5 , 7) $

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$f(x)=\frac{5}{2} x-\frac{11}{2}, 1 \leq x \leq 5$

02:19

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 1

Four Ways to Represent a Function

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Will B.

September 24, 2022

Find the domain of the function whose range is this line segment. (Enter your answer using interval notation.)

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Lectures

04:31

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.

12:15

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.

09:15

Find an expression for the…

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\begin{equation}\begin…

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$51-56$ Find an expression…

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Find a formula for the fun…

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01:06

$45-50$ Find an expression…

03:00

Find a function whose grap…

06:14

All right, let's find the function that is the line between these two points. So in order to get the equation of a line, we need the slope and the Y intercept. So to get the slope, we can use our slope formula. Why? To minus y 17 minus negative three over X two minus x 15 minus one. And that gives us 14th which reduces to five house. And now we confined the Y intercept. So let's use point slope form, which is why minus y one equals M times X minus X one. And we could use either one of our two points. I'm just going to use the 2nd 1 so we have y minus seven equals five halves times a quantity X minus five. If we want to change this equation into slope intercept form, we can start by distributing the five halves. So why minus seven equals five halves X minus 25 halves, and then we can add seven to both sides, adding seven is like adding 14 halves, so we end up with y equals five halves minus 11 house. So that's the equation of the line through those two points. And because we just want this segment, we're going to restrict the domain and we're only going to go from X equals 12 x equals five.

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