Answer:
1.44
Step-by-step explanation:
1.63-.19= 1.44
Answer:
a horizontal translation by 3 units left
Step-by-step explanation:
f(x)= |x|
we are given with absolute function f(x)
g(x) = |x+3|
To get g(x) from f(x) , 3 is added with x
If any number is added with x then the graph of the function move to the left
Here 3 is added with x, so the graph of f(x) moves 3 units left to get g(x)
So there will be a horizontal translation by 3 units
If
is an integer, you can use induction. First show the inequality holds for
. You have
, which is true.
Now assume this holds in general for
, i.e. that
. We want to prove the statement then must hold for
.
Because
, you have
and this must be greater than
for the statement to be true, so we require
for
. Well this is obviously true, because solving the inequality gives
. So you're done.
If you
is any real number, you can use derivatives to show that
increases monotonically and faster than
.
Answer:
3 points
Step-by-step explanation:
in a function, an x-value must have only one y-value correlated with it.
So, you would need to remove either (-3, 2) or (-3, 3)
And, you would need to remove either (2, -2) or (2, -4)
<em>And, </em>you would need to remove either (1, 4) or (1, -4)
So--you need to remove 3 points in total for this to be a function.
[a y-value can have multiple x-values. the two points at -4 are allowed, and do not need to be removed for both of them to be there]
To figure this out, we just need to plug in the points.
4(-1) - 2(-2) = 0
-4 - (-4) = 0
-4 + 4 = 0
0 = 0
True
The correct answer is a. (-2, -1).
