1. Choose all the point(s) of discontinuity (limitations/restrictions) for the rational function x-1 y – x²-7x+10 * a. x=5 b. x=-2 C. X=-5 d. x 2 2. Simplify the expression 8x+15 4x+20 State any restrictions on the variable. 4(x+5) a. x+3 X# - 3 b. 4(x+5) X - 5 X+3 1 C. , X - 3 d. , X - 3, - 5 3. Find the difference of - 3(x-21) a. (x+7)(x-7) b. (x+7)(x-7) C. 3x-2 d. 3x-63

Q: Consider the rational function y = 7x 12 3x - 2 Which one of the following is true? Select one…

A: Given :Rational function :y=7x-123x-2

Q: 18. Determine the domain restrictions for the rational function below. y= 6 2+5 Ox-5 Oz #5 02-6 Oz‡6

A: domain means which x value we can put in equation so function is define y = 6/(x+5) function is only…

Q: Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DNE.)…

A: To find x-intercept, substitute r(x)=0 and solve it:

Q: 10x For the above rational function f( x ) identify its three inflection points. 2.5x2 + 2 lowest =…

A: Given function f(x)=10x2.5x2+2 ⇒f(x)=10x52x2+2⇒f(x)=20x5x2+4 Differentiating,…

Q: 31 2 -4 -3 -2 -1 2 3 17x For the above rational function f( x ) = identify its three inflection…

A: in the question it is asked to calculate the inflection points for the rational function f(x) =…

Q: 10. Match the graph of the rational function given by ax + b f(x) cx + d with the given conditions.…

A: f(x)=ax+bcx+d Match the graph with the given conditions (i)a>0,b<0,c>0,d<0  ---- graph c…

Q: Suppose that two functions f(r) and g(z) are defined by f(2) = 1° +8 and g(z) = r+2

A:

Q: 2- -5 -4 -3 -2 -1 16 For the above rational function f( x ) = identify its three inflection points.…

A: The given rational function is: fx=16x3x2+4 To find the inflection points, equate this to zero.…

Q: 4. For the interval of decrease of the rational function y = (x-3)/ (2x - 6), Ara says (3, + o0) is…

A: A function is increasing in an interval, if f(x1)<fx2 for x1<x2. A function is decreasing in…

Q: State the domain of the rational function. x-9 8) f(x)= x2.5 A) (, -) O--,-3)u(-3,3)u (3, ) B)…

A: To find the domain of the below rational function. fx=x−9x2+5 fx=11x+5

Q: The x-intercept of the rational function r(x) = 2x+6 is x-5 a) (5,0) b) (-5,0) c) (3,0) d) (-3,0) e)…

A:

Q: 3x – 3 - Analyze the rational function y %3D 6 – x

A: This is a problem of analysis of a function. To get the stationary and inflection points. Also, in…

Q: Match the following rational functions with their graphs. Place the appropriate letter in the space…

A:

Q: 4. Determine if the rational function has a hole. If it does, find the coordinates. x + 3x g(x) : х3…

A: Yes, the rational function has hole. The coordinates of hole is (0 ,12 )

Q: Explain how to obtain the rational function g(x) = from the parent function f(x) = !

A: Let's find.

Q: Consider the rational function f(x)=x−4x2+2x+14  A: write a ratio of monomial expressions that best…

A: The given rational function is,

Q: Find the limit of the following rational function as (a) x→o and (b) x→ - o. 3 2 - 4x° - 4x + 3 h(x)…

A:

Q: Suppose the cost (in dollars) of removing p% of the pollution in a river is given by the rational…

A: fp=56,000p100-p a). Put p=50 in fp=56,000p100-p, we get f50=56,00050100-50=$56,000 Therefore cost of…

Q: 6x + 3a + 13z O D 5. Determine the end behavior of the rational function f(x) 74 + 22 O approaches y…

A:

Q: In a rational function, as x⟶∞,y⟶∞.  It follows that the rational function has ___________ Suppose…

A:

Q: B. Write a rational functionf that has the specified characteristics. c Vertical asymptote: x = 0…

A:

Q: For what interval(s) is the graph of the rational function positive and increasing? 4 4 a) for no…

A:

Q: f (x) = 2+x-2 1 -1

A:

Q: Given a rational function f, when x=4, the value of f(x) is. 1.32. Thus we know that…

A: Given query is to find the correct option for the function.

Q: 9. The graph of which of the following rational functions has a hole? 2х - 6 y = 2х - 6 2х - 3 2х —…

A: As this is a multiple question, according to the Bartleby answering rule, only first question is to…

Q: Consider the rational function f(x)=8x+15/2x−13. part a=8x ,part b =2x   Using your results from…

A:

Q: 20x For the above rational function f( x ) = identify its three inflection points. 2x2 + 1 lowest =…

A:

Q: What is the equation of the slant asymptote of the rational function? f(x) = 10x³-15x²+x-1 5x²-2 11…

A:

Q: Where (for what values of x) does the rational function (x + 28)(x – 92) f(x) 12 x + 97)(x + 16)(x +…

A: Let f(x)=p(x)q(x) be a rational function then if p and q have a common factor (x-a) that…

Q: Find the oblique asymptote of the rational function ( 2-z-20) (z+5z+6) f (1) = (z+4)(2z²-9r-5)

A:

Q: What is the equation of the rational function g(x) and its corresponding slant asy -10-9-8 O O O 7…

A: Given: Graph:

Q: Find the domain of the rational function: h(x) = (x + 5)/(x2 + 25)

A: h(x)=x+5x2+25

Q: Sketch the graph of each rational function by hand. 10아 I. 4x-6 1. f(x)3= %3D 2x +5 8 6 2 6. 8 10 2.…

A: To draw the graph of given rational function

Q: The rational function 2t + 2 gives the number of hours it will take two pipes, working together, to…

A:

Q: Sketch the graphs of the rational functions y = x2/x2 - 4

A: Given the function y = (x2)/(2x- 4). We need to plot the graph for the above function.

Q: Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DI x² – 4…

A: To find the x and y-intercept of the below function. rx=x2−4x2

Q: Find the domain of the rational function: f(x) = (x2 - 25)/(x - 5), b. g(x) = x/(x2 - 25)

A: (a) Consider the provided function, fx=x2-25x-5 Find the domain of the rational function. The domain…

Q: Suppose the cost (in dollars) of removing p% of the pollution in a river is given by the rational…

A:

Q: find the end behavior for this rational function:. (3x^2 + 15x - 42) ÷ (x^2 - 25)

A: Let fx=3x2+15x−42x2−25 We have to find the end behavior that is check at ±∞ Now,…

Q: The rational function Re) = %3D 2t + 2 2+ 2t gives the number of hours it will take two pipes,…

A: Solution

Q: The x-intercept of the rational function r(x) 2x+6 is x-5 %3D a) (5,0) b) (-5,0) c) (3,0) d) (-3,0)…

A: The given rational function is: rx=2x+6x-5 The x-intercept is a point on the x-axis, where the graph…

Q: Sketch the graphs of the rational functions y = x4 - 1/x2

A: Given:         y=x4−1x2

Q: Sketch the graphs of the rational functions y = x3 + 2/2x

A: we have to sketch of the rational function y=x3+22x

Q: Sketch the graphs of the rational functions y = x2 - 4/x2 - 3

A:

Q: -5 -4 -3 -2 3 4 3 -4+ 18x For the above rational function f( x) = identify its three inflection…

A: It can be solved using differentiation.

Q: Over what interval is the graph of the rational function positive but decreasing? y 4 2 -4 0 2

A:

Q: Use the graph of the rational function below to answer the questions. 10 la As-l-, f(x) → 1b ASX-r,…

A: It is observed that from the figure, f(x) has the vertical asymptote at x = 1 and horizontal…

Q: For what interval is the graph of the rational function decreasing? *VA is x=-3 A. for no values…

A: Given the graph of the rational function is

Q: Where (for what values of x) does the rational function (x – 3)(x + 4) - f(x) = 36 (x + 74)(x – 3)(x…

A:

Q: Recall that the domain of a rational function A2 is all values of x except those values for which…

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.