Question

Graph and analyse:

y=log3x ----->y=2log3(x-1)

Answer #1

Graph of y= logx

To plot y= log (3x), we shrink the graph of y=logx, 3-units along X-axis and get the following

Obviously log(3x)= 0 if x=1/3=.33333

Next, to plot y= 2log3(x-1), we do the following steps

1) shift the grapgh of y=logx, 1- unit toward right.

2) Shrink the graph of y=log(x-1), by 3-unit along X-axis.

3) Finally, we stretch the graph of y=log3(x-1) by 2-unit along Y-axis. Figure of the graph of y= 2log3(x-1) is given below

Graph y = x3 and y = x on [0, 2].
1) graph of the area between the curves y = x3 and y
= x on [0, 2] includes _____________
distinct areas.
2) One of my shaded areas has area =
3) One of my shaded areas has area =
4)
The graph showing the area between the two curves y =
x3 and y = x has four intersection points. Which of the
following points is not an intersection...

Find
Domain
x-int
y-int
VA
HA
Hole
Sign graph
graph
a-) y=1/x2+3x-10
b-) y=x+2/(x+2)(x-3)
c-) y=x-1/x2-2x+1
d-) y=-2/x

3.Let P = (x,y) be a point on the Graph of y = 1/x.
3a.Indicate why, on the basis of Concavity and Symmetry, the
points P = (1,1) and (-1,-1) must be closest of all points P on the
Graph to the Origin.
3b.Find the closest point P on the graph to (2,2).

1-) Find:
Domain
x-int
y-int
VA
HA
Hole
Sign graph
graph
a-) y= 5x-2/x+2
b-) y= (5/x+3) -4

1. The graph of y = f(x) = 1/ x^2 , 1 ≤ x < ∞, is rotated
around the x-axis.
(a) Calculate the resulting volume.
(b) Set up the integral that gives the resulting surface area,
but DO NOT WORK OUT THE INTEGRAL.

1-) Find:
Domain
x-int
y-int
VA
HA
Hole
Sign graph
graph
a-) y= x2-9/2x+6
b-) y= 3x/x3-x

if
y' is equal to (2x-4)^2(x+1)^3, find y'' and draw the graph of
y.

Consider function f(x, y) = x 2 + y 2 − 2xy and the 3D graph z =
x 2 + y 2 − 2xy. (a) Sketch the level sets f(x, y) = c for c = 0,
1, 2, 3 on the same axes. (b) Sketch the section of this graph for
y = 0 (i.e., the slice in the xz-plane). (c) Sketch the 3D
graph.

Consider the graph of y=f(x)=1−x2 and a
typical point P on the graph in the first quadrant. The tangent
line to the graph at P will determine a right triangle in the first
quadrant, as pictured below.
a) Find the formula for a function A(x) that computes the area
of the triangle through the point P=(x,y)
b) Find the point P so that the area of the triangle is as small
as possible: P =()

If X, Y are topological spaces and f : X → Y we call the graph
of f the set Γf = {(x, f(x)); x ∈ X} which is a subset of X ×
Y.
If X and Y are metric spaces and f is a continuous function
prove that the graph of f is a closed set.

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