13) Given that y = 2- show that is x² -2x+4 always positive for all real values of x. Sketch the curve y f(x), showing clearly the %3D asymptotes, intercepts with the coordinate axes and the behaviour of the curve as it approaches it asymptote(s).

Q: 5. Sketch the reciprocal of y= (x- 1)'(x + 3) (x- 4) (Label intercepts, all asymptotes clearly, if…

A: Given that: y=(x-1)3(x+3)2(x-4)

Q: x-sin x f(x) = x²–1

A: f(x)=xsinxx2-1For Vertical aymptotesEquate denominator to zero⇒x2-1=0⇒(x+1)(x-1)=0⇒x=-1,1 Vertical…

Q: Find the horizontal and vertical asymptotes of the curve. x2 + 1 y = 9x2 - 26x – 3 (smaller x-value)…

A: From the given problem: y=x2+19x2-26x-3 To calculate vertical asymptote, equate denominator to zero…

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A: Consider the function: y=ax2+4x-b. such that a,b>0. Find the equation for all horizontal and…

Q: 8. Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check…

A:

Q: y = 2x / 1-x2 Asymptotes, critical points, extreme points of the curve, By finding the turning…

A: To find, asymptotes, critical points, extreme points of the curve, By finding the turning points and…

Q: 22. Sketch the graph as described as: x-intercepts at (4, 0) and (-3, 0) y-intercept at (0, -6)…

A: graph of given function is given below...

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A:

Q: ample 3: Sketch the graph of the curve y-Ax)-x-1

A: See the attachment

Q: Find the horizontal and vertical asymptotes of this curve. 2x²+x-1 y= = x²+x-2

A: Given.

Q: y = 2x / 1-x2 Asymptotes, critical points, extreme points of the curve, By finding the turning…

A:

Q: G&)= In (5x t10) + 1, 1 State and domain, vertical asymptote end behavior. As approches vertical, Gx…

A: Let G(x)=ln(5x+10)+1.1 The domain of the function is the set all x-values on which the function is…

Q: 3) y =x² +2x - T 4) y=x² – 8x + 14 2.5 1.5 0.5 -1 -0.5 -3 Find EXACT Vaiue's of x- intercepts For…

A:

Q: Find the horizontal and vertical asymptotes of the curve. 2e* ex - 5 y = X = y =0 (smaller y-value)…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: y6_y²+7 h (y) y2+3y

A:

Q: Find the horizontal asymptotes.

A: ft=et1+e-t Now as t→∞, ft→∞. & limt →-∞ft=limt →-∞et1+e-t=limt →-∞et0-e-t        By using…

Q: Find the coordinates of the point where the graph of f(r) = 2 i12 crosses its slant asymptote and…

A: For the solution of the problem follow the next step.

Q: C. Find the horizontal and vertical asymptotes of the curve y = x+ 4

A:

Q: Predict the location of vertical and horizontal asymptotes; holes; x and y intercepts. Show your…

A: Asymptote of a curve is a line whose distance with the curve tends to zero as the x or y or both…

Q: 6x Find all horizontal asymptotes of f(x) = V4r2 - 10 Oy=+3 oy = 6 only Oy = 0 oy = ±6

A:

Q: Find the equation of all its vertical asymptotes given the cosecant function y = csc 2 csc-) 3.

A: The given function is y=cscx2-π3. Obtain the vertical asymptotes by solving sinx2-π3=0 as follows.

Q: Find the horizontal and vertical asymptotes of the curve

A: Given curve: y=x+3x+2

Q: 3. Find all the asymptotes to the curve, hint, there are more than one and they are all horizontal!…

A: 3.The given function is y=x6+64-x6-2x3+10 Note:   Multiple questions are given, we are answered with…

Q: ) Identify the horizontal and verical asymptotes of y = f(x) where %3D 2x2 – 4x – 30 f (x) 5x3 –…

A:

Q: Draw the curve if y' is negative and y'' is positive on the interval of (2,3), while y' is positive…

A:

Q: Jse the guideline in §4.4 to sketch the curve: f(x) = 2x3 + 3x2 – 120x. 4). Domain, Symmetry,…

A:

Q: Sketch the curve of the function f(x) = (x² – 4x – 5)/(x² + x) %3D - SHOW ALL WORK FOR THE FOLLOWING…

A:

Q: 3x2 + х — 3 у x? +х — 6

A: We are asked to find horizontal and vertical asymptote.

Q: 2.x2 + 16x + 30 Find the horizontal and vertical asymptotes of the curve y = x² + x – 20

A: We have to find the asymptate

Q: Find all horizontal and vertical asymptotes of the curve of 3ex+2e=x f(x) = 2ex-5e-x Show all your…

A: A line y=L is said to be the horizontal asymptote of the curve y=f(x) if  limx→−∞f(x)=L or…

Q: How do you solve this and can you show me step by step?

A:

Q: I. Analyze and sketch the following curves. Indicate the intercepts, asymptotes, & critical points…

A:

Q: 14. What does it mean to say that the line x = a is a vertical asymptote of the curve y = f(x)? Draw…

A:

Q: Given the following curve: y= (2x4+5x3-36x2-41x+70)/(x2-x-12) 1. What is the horizontal asymptote…

A: The function is given as:y=2x4+5x3−36x2−41x+70x2−x−12The objective is to find the asymptotes of the…

Q: 11. The maximum point of the curve * y =r' - 3r° + 4 is at

A:

Q: Can you help with this problem step by step?

A: Given: -

Q: 1. Find the maximum point of the following curve. <press your answer in this form (#,#) or N/A if…

A: Differentiate the given function with respect to x and then solve y'= 0 to obtain the critical…

Q: Find the horizontal and vertical asymptotes of the curve together with concavity and intervals of…

A:

Q: find the horizontal and vertical asymptotes of the curve y=x+3/x+2

A: The given equation of the curve is: y=x+3x+2 The denominator of this equation is undefined at x=-2.…

Q: Find the horizontal and vertical asymptotes of the curve. 5x2 + x-6 x2 + x - 42 y= x=1-6 X (smaller…

A: To determine the equations of asymptotes (ifany) of the given rational curve

Q: The horizontal asymptotes of the curve 9x y = (zª + 1)'/4 are given by and Yı Y2 = where y1 > Y2-

A: Here, the given function is: y=9xx4+114

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A:

Q: 5. Determine the equations of the vertical asymptotes 1 S(x) = %3D x² - 8x + 12

A:

Q: 1– sin(x) - Find all horizontal asymptotes of y x2

A: The horizontal asymptote of a curve is the line such that the distance between the line and the…

Q: Find the horizontal and vertical asymptotes of the curve. 5x + 4 y = х— 6

A: The process to find the asymptotes has been shown in the next step.

Q: 2. Determine an equation in the form f (x) for a function with a vertical asymptote at x = -2 and a…

A:

Q: Find the coordinates of the point where the graph of f(z) = 2-10+12 crosses its slant asymptote and…

A:

Q: 5. (a) Write down a function that has vertical asymptotes at the points r = 1, x = 2, and r = 3, and…

A: 5 (a) Consider the function f(x) has vertical asymptotes at the points x=1, x=2, and x=3, and a…

Q: 2.x and sketch the graph. RRD 4. Find intercepts and asymptotes of f(x): %3D x+2

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: