Answer:ed44
Step-by-step explanation:
Answer:
y
=
4
(
1
2
)
x
Explanation:
An exponential function is in the general form
y
=
a
(
b
)
x
We know the points
(
−
1
,
8
)
and
(
1
,
2
)
, so the following are true:
8
=
a
(
b
−
1
)
=
a
b
2
=
a
(
b
1
)
=
a
b
Multiply both sides of the first equation by
b
to find that
8
b
=
a
Plug this into the second equation and solve for
b
:
2
=
(
8
b
)
b
2
=
8
b
2
b
2
=
1
4
b
=
±
1
2
Two equations seem to be possible here. Plug both values of
b
into the either equation to find
a
. I'll use the second equation for simpler algebra.
If
b
=
1
2
:
2
=
a
(
1
2
)
a
=
4
Giving us the equation:
y
=
4
(
1
2
)
x
If
b
=
−
1
2
:
2
=
a
(
−
1
2
)
a
=
−
4
Giving us the equation:
y
=
−
4
(
−
1
2
)
x
However! In an exponential function,
b
>
0
, otherwise many issues arise when trying to graph the function.
The only valid function is
y
=
4
(
1
2
)
x
Answer
41/12
Step-by-step explanation:
convert mixed numbers into improper fractions 21/4-(3-7/6)
calculate 21/4 - 11/6
subtract fractions 41/12
Answer: Choice D.
Max: f (-1,-2)=4; min:f(3,5)=-11
----------------------------------------
----------------------------------------
Work Shown:
Plug in (x,y) = (-1,3)
f(x,y) = -2x-y
f(-1,3) = -2*(-1)-3
f(-1,3) = 2-3
f(-1,3) = -1
------------------
Plug in (x,y) = (3,5)
f(x,y) = -2x-y
f(3,5) = -2*3-5
f(3,5) = -6-5
f(3,5) = -11
------------------
Plug in (x,y) = (4,-1)
f(x,y) = -2x-y
f(4,-1) = -2*4-(-1)
f(4,-1) = -8+1
f(4,-1) = -7
------------------
Plug in (x,y) = (-1,-2)
f(x,y) = -2x-y
f(-1,-2) = -2*(-1)-(-2)
f(-1,-2) = 2+2
f(-1,-2) = 4
------------------
The four outputs are: -1, -11, -7, and 4
The largest output is 4 and that happens when (x,y) = (-1,-2)
So the max is f(x,y) = 4
The smallest output is -11 and that happens when (x,y) = (3,5)
So the min is f(x,y) = -11
This all points to choice D being the answer.
