The graph located in the upper right corner of the image attached shows the graph of y = 3[x]+1.
In order to solve this problem we have to evaluate the function y = 3[x] + 1 with a group of values.
With x = { -3, -2, -1, 0, 1, 2, 3}:
x = -3
y = 3[-3] + 1 = -9 + 1
y = -8
x = -2
y = 3[-2] + 1 = -6 + 1
y = -5
x = -1
y = 3[-1] + 1 = -3 + 1
y = -2
x = 0
y = 3[0] + 1 = 0 + 1
y = 1
x = 1
y = 3[1] + 1 = 3 + 1
y = 4
x = 2
y = 3[2] + 1 = 6 + 1
y = 7
x = 3
y = 3[3] + 1 = 9 + 1
y = 10
x y
-3 -8
-2 -5
-1 -2
0 1
1 4
2 7
3 10
The graph that shows the function y = 3[x] + 1 is the one located in the upper right corner of the image attached.
y varies inversely with x.
Example:
If we multiply x by 2 we need to divide y by 2 too.
So,
If y = 16 and x = 1/2, find y when x = 32
Lets see, from 1/2 to 32 e need to multiply 1/2 by 64, right? So let's divide 16 by 64.
16/64 = 8/32 = 4/16 = 2/8 = 1/4
So we can say that:
If y = 16 when x = 1/2, y = 1/4 when x = 32.
The coefficient is the number, therefore -5 and -4,
The exponent of the first x is 1 and the second x is 2, if the 2 is meant as an exponent. The first exponent of y is 1 and 5e second y is 2
X^2+y^2 = 16
can be written as
(x-0)^2+(y-0)^2 = 4^2
We see that the second equation is in the form
(x-h)^2 + (y-k)^2 = r^2
where
(h,k) = (0,0) is the center
r = 4 is the radius
The polar form of the equation is simply r = 4. Why is this? Because the radius is fixed to be 4 no matter what happens with theta. As theta goes from 0 to 360, the points generated all form a circle centered at (0,0) with radius 4.
Answer: r = 4
