Answer:
Option C and D that is y= tan x and y= cot x
Step-by-step explanation:
The range is the values of y means the values that y can take in a function:
So, range of tan x and cot x are all real numbers.
Period of tan x is
Period of cot x is
Option A and B that is secx and csc x are discarded
Answer with explanation:
Given a function, y=f(x)
The Set of values that ,x can take for which y is defined is called domain of the function.
And,the set of values that ,y can take for which x ,is defined is called range of function.
For example:→Consider the function, y=x²
→y is defined for all values of x,so Domain is set of real numbers.→(-∞,∞)
→x is defined for positive values of y,so range of this function is [0, ∞).
A:→ y =sec x
Range =(-∞,-1]∪[1,∞)
B: →y=Cosec x
Range =(-∞,-1]∪[1,∞)
C:→y=tan x
Range =(-∞,∞)
D:→y=cot x
Range=(-∞,∞)
→→Option C and D⇒Tan x and Cot x, are trigonometric function ,whose range are set of all Real Numbers.
Answer:
The volume of the solid is 19. unit³
Step-by-step explanation:
The given function is y = x³
The solid is created by revolving R about the line y = 1
We have that when y = 1, x = 1
Taking the end point as x = 2, we have the volume given by the washer method as follows;
Where;
a = 1, and b = 2, we have;
g(x) = 1
The volume of the solid, V = unit³ = 19.
unit³
The coordinates of the image of triangle are transformation are X = (1,3), Y = (5,-3) and Z = (-1, -7)
<h3>How to determine the transformation?</h3>From the figure, the coordinates of the triangle are:
A = (-1, -1)
B = (1, 2)
C = (-2,4)
The transformation rule is given as:
This means that, we start by dilating the triangle by a scale factor of 2.
So, we have:
A' = (-2, -2)
B' = (2, 4)
C' = (-4,8)
Next, we rotate the triangle across the x-axis
So, we have:
A'' = (-2, 2)
B'' = (2, -4)
C'' = (-4,-8)
Lastly, we translate the triangle by (x + 3,y + 1) to get the triangle XYZ
So, we have:
X = (1,3)
Y = (5,-3)
Z = (-1, -7)
See attachment for the image of the transformation
Read more about transformation at:
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