Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

(a) Find the $x$ -intercept(s); (b) Find the vertical asymptotes; (c) Find the horizontal asymptotes. (d) Sketch the graph.$$f(x)=(2 x-3)(x-1)$$

(a) $x=3 / 2$(b) $x=1$(c) $y=2$$(d)$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 4

Limits at Infinity, Infinite Limits and Asymptotes

Derivatives

Missouri State University

Campbell University

Oregon State University

Baylor University

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

02:15

(a) Find the $x$ -intercep…

02:07

03:04

02:33

02:19

02:32

08:03

02:25

04:09

02:38

02:21

02:40

02:28

02:20

05:48

(a) Determine the $x$ -int…

01:09

01:45

For the graph of $y=f(x)$<…

and this problem, we're going to be finding the X intercept vertical ascent. Oh and horizontal. A sum total of the function. Two x minus three divided by x minus one. In hopes of being able to sketch a graph at the end. So starting with part A we want to find that X intercept and to do that, we're just going to take our entire function. So two x minus three divided by x minus one. We're gonna set it equal to zero and then solve for X. You can see here, we can multiply both sides by x minus one. We're left with two. X minus three is equal to zero, add three to both sides, two X is equal to three and then divide both sides by two. You can see we're going to have an intercept at X is equal to three halves. So we can go ahead and plot that. And that is what about 1.5? So it's going to sit right in here and then for part B we want to find our vertical ascent oats and then finding vertical ascent owes its important really. Just to look at our denominator so x minus one. We can just set that equal to zero and solve for X. So here we have X is equal to one for a vertical aspect to it. So we can go ahead and sketch that as well. So we're really just giving ourselves these outlines so we can draw our curves part C. We want to find our horizontal Asato and hear what we really need to look at is these dominant terms of both the numerator and denominator. So in the numerator we have two X. Denominator, we have X. Simplifying this. You can see our exes are going to cancel out and we're just left with two. So at Y is equal to two. We have a horizontal ass until it so that will sit right in here. And now we can sketch a graph. We don't necessarily know just based on the information we have, the direction of or the exact point at which are curves are going to actually change direction. But you can just grab that in your graphing calculator to give yourself a better idea of what you'll see is that it does follow these outlines we gave ourselves, we are going to stay within these ascent oats and we're going to go through that X intercept at three halves and then another one up top here again is going to follow these ass and tools that we gave ourselves and your graph will look something like this.

View More Answers From This Book

Find Another Textbook

02:50

Find the points on the curve $$y=2 x^{3}-54 x+1$$ at which the tangent line …

01:36

Locate all critical points.$$s(t)=2 t^{3}-9 t^{2}-60 t+5$$

01:52

$$f(x)=\left\{\begin{aligned}4 x-2 & \text { if } x \leq 1 \\x+1 & \…

04:48

Determine an equation for the line (a) parallel (b) perpendicular to $3 x+7 …

03:23

Let $A\left(x_{1}, y_{1}\right)$ and $B\left(x_{2}, y_{2}\right)$ be in any …

03:20

A 6 foot man walks away from a light sitting atop a pole 16 feet above groun…

Use the first derivative to determine where the given function is increasing…

03:24

The sum of two positive numbers is $100 .$ what should the numbers be if the…

04:53

Determine an equation for the line (a) parallel (b) perpendicular to $2 x-5 …

01:11

Suppose that, in the development of the definition of the derivative, we wro…