Determine whether the graph of the equation y = x3 - 1 is symmetric with respect to the y-axis, the x-axis, the origin, more than one of these, or none of these.

Q: Find the x- and y-intercepts of the graph of the equation y2 = x + 1.

A: Given equation - y2 = x+1                .........(1)x-intercept,Putting y=0,02 = x+1x+1 = 0x…

Q: Sketch the graph of the equation, and label the x- and y-intercepts

A: Given equation is x=3y+4. To sketch the graph of the equation and label the x-intercept and…

Q: Determine whether the graph of equation y2 = x2 - 2 is symmetric with respect to the y-axis, the…

A:

Q: Determine if the graph of the equation is symmetric to the y-axis, x-axis, origin, or none of these.…

A: Given function is

Q: Determine whether the graph of equation y = 2x + 3 is symmetric with respect to the y-axis, the…

A: y-axis: To find the symmetricity about the y-axis, we plug -x in place of x.  y=2(-x)+3 or y=-2x+3…

Q: Find the x- and y-intercepts of the graph of the equation y = x√(4 − x2).

A: The x intercept is the coordinate which could be found by substituting 0 in place of y and obtaining…

Q: Find the x- and y-intercepts of the graph of the equation y = √(x + 4).

A: We need to Find the x- and y-intercepts of the graph of the equation y = √(x + 4).

Q: Determine whether the graph of equation x2 - y3 = 2 is symmetric with respect to the y-axis, the…

A: To check symmetry about the y-axis, we will plug -x in place of x.  We get the same equation back.…

Q: Determine whether the graph of the equation is symmetric with respect to the y-axis,the x-axis,the…

A:

Q: Determine whether the graph of the equation y = x2 + 8 is symmetric with respect to the y-axis, the…

A: Given equation y = x2 + 8

Q: Determine whether the graph of the given equation is symmetric with respect to the y-axis, the…

A:

Q: Determine which of the given points are on the graph of the equation.

A: Given :            The equation y = x3 - 2x         Points: 0, 0 ; (1, 1) ; (1, -1)   To determine…

Q: Determine whether the graph of x2 - y3 = 2 is symmetric with respect to the y-axis, the x-axis, the…

A: To check the symmetry about the y-axis we plug -x in place of x.  We get the same equation back. So…

Q: Determine whether the graph of the given equation is symmetric with respect to the y-axis, the…

A: We have given the function; y2 = x2 + 6

Q: Determine whether the graph of the given equation is symmetric with respect to the y-axis, the…

A: Consider the following equation:

Q: Determine whether the graph of each equation is symmetric with respect to the origin. (a) x2 + y2 =…

A: We have to determine whether the graph of each equation is symmetric with respect to theorigin.…

Q: Determine whether the graph of equation y = x2 + 6 is symmetric with respect to the y-axis, the…

A: Given: y=x2+6 given equation is a equation of upward parabola as coefficient of x2 is positive now…

Q: Determine whether the graph of the given equation is symmetric with respect to the y-axis, the…

A: We know that x2+y2=a2  represent a circle withcentre (0,0) and radius rHere  x2+y2=100…

Q: Determine whether the graph of the below equation is symmetric with respect to the y-axis, the…

A: To test symmetry we have fellowing rules y axis : put x = -x  if the function is still equal to…

Q: Determine whether the graph of the equation is symmetric with respect to the x- axis, the y-axis,…

A: Given query is to find axis of symmetry.

Q: Make a table of values, and sketch a graph of the equation. y = -2x

A: y=-2x we have to make a table of values and then sketc a graph

Q: 1. x+y-z 5 IN

A:

Q: Determine whether the graph of equation x = y2 - 2 is symmetric with respect to the y-axis, the…

A: Given: x=y2-2 for finding symmetry of given function we draw the graph of given expression and check…

Q: The x-intercepts of the graph of an equation are those x-values for which ..........

A: Given: The x-intercepts of the graph of an equation are those x-values for which ..........

Q: Determine whether the graph of equation x2 + y2 = 49 is symmetric with respect to the y-axis, the…

A: Given equation: x2+y2=49 Testing of symmetry rules: X-Axis symmetry: In the equation, replace y with…

Q: Determine whether the graph of equation x = y2 + 6 is symmetric with respect to the y-axis, the…

A: The given equation is x=y2+6. Replace x with -x and check the symmetry about y axis. -x=y2+6x=-y2+6…

Q: If the graph of an equation is symmetric with respect to the y-axis and - 4 is an x-intercept of…

A: Answer:(4,0)

Q: Determine whether the graph of the given equation is symmetric with respect to the y-axis, the…

A: Given that the equation: y4=x3+6 Symmetry about x-axis The graph of the equation is symmetric about…

Q: Sketch the graph of the equation, and label the x- and y-intercepts

A: Consider the given equation. y=-2x-3 Put x=0 in the equation to find the y-intercept. y=-20-3=-3…

Q: Determine whether the graph of the given equation is symmetric with respect to the y-axis, the…

A: The given equation is  y2=x2 -2.

Q: Sketch the graph of the equation, and label the x- and y-intercepts

A: Given y=14x

Q: State the equation of a relation whose vertex would be lower than the origin and to the left of the…

A: We have to find the equation of the relation whose vertex is lower than the origin and left to the y…

Q: Determine whether the graph of equation x2 + y2 = 100 is symmetric with respect to the y-axis, the…

A: Given that, The equation x2 + y2 = 100 We have to check that the graph of a given equation is…

Q: Determine whether the graph of y = x3 is symmetric with respect to the y-axis, the x-axis, or the…

A: Given: y=x3 for finding symmetry of given expression, we sketch the graph of given expression as…

Q: Determine whether the graph of the equation x3 - y2 = 5 is symmetric with respect to the y-axis, the…

A: Given, x3-y2=5

Q: Determine whether the graph of equation y = 2x + 5 is symmetric with respect to the y-axis, the…

A: We have to determine whether the graph of equation y = 2x + 5 is symmetric with respect to the…

Q: Determine whether the graph of the given equation is symmetric with respect to the y-axis, the…

A: Solution:- The graph is  x3-y2=5 we have to test either the graph is symmetrical about y-axis,…

Q: Determine whether the graph of the given equation is symmetric with respect to the y-axis, the…

A: Considering the given equation:→ y=x2-2 -(i)Our Aim is to determine whether the graph of equation is…

Q: Determine whether the graph of equation y = x2 - 2 is symmetric with respect to the y-axis, the…

A: Graph of a function: We need to draw the graph of the function y=x2-2

Q: Identify the graph of the given equation. 3x2 = y2 - 1

A: The given equation is 3x2=y2-1. Rewrite the above equation as follows. 3x2=y2-1y2-3x2=1y21-x213=1

Q: Identify the graph of the given equation. 3x2=y2-1

A: Identify the graph of the given equation. 3x2=y2-1 The graph is a hyperbola with vertices (0, 1) and…

Q: Sketch the graph of the equation, and label the x- and y-intercepts

A: The given equation is, y=x3-8 To find the x-intercept of the curve, y=0 0=x3-8x3=8x=83=2 hence, the…

Q: Sketch the graph of the equation, and label the x- and y-intercepts

A: y=x

Q: Sketch the graph of the equation, and label the x- and y-intercepts

A: To graph the equation

Q: Sketch the graph of the equation, and label the x- and y-intercepts

A: Given:                 x+5=0 Rewrite:                y=x+5 x y 0 5 -5 0 1 6 -1 4

Q: Determine whether the graph of the given equation is symmetric with respect to the y-axis, the…

A: Given function is y=x2+6. To determine whether the graph of the given equation is symmetric with…

Q: Determine whether the graph of the given equation is symmetric with respect to the y-axis, the…

A: Here We have to determine whether the graph of the given equation is symmetric with respect to the…

Q: Make a table of values, and sketch a graph of the equation. 4y = -x2

A: Given: 4y=-x2

Q: Sketch the graph of the equation, and label the x- and y-intercepts

A: Consider the given equation y=4x

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.