Step-by-step explanation:
The domain of a function is all possible input x-values, and the range of function is all possible output y-values.
The domain of this function is (-6, 3) and the range is (-5, 5). Those are written like this:
D: (-6, 3)
R: (-5, 5)
I suppose I'll pick the first one: "The domain is (-6, -1)." This is wrong as the domain on the graph shown is (-6, 3).
Answer
y = 1(x +1) - 3
Explanation
A quadratic equation of the form y = ax^2 + bx + c
This written in complete the square form provides you with the vertex (either a maximum or minimum point depending on the equation).
This results in y = a(x + p) + q
Where - p is the x value and q is the y value of turning point.
For graph 22, x = -1 and y = -3
Therefore, the equation is of the form
y = a(x + 1) - 3 (*)
We still need the value a, this can be obtained by using the y-intercept we are given.
We are told x = 0 when y = -2
Substitute this in (*) equation:
-2 = a(0+1) - 3
-2 = a - 3
a = 1
Therefore final equation is
y = 1(x +1) - 3
This should provide you with the train of thought of how the second question should also be tackled.
If unsure about why the equation
y = a(x + p) + q gives the vertex ask in comments I will respond
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:
AD is congruent to RS
Step-by-step explanation:
we know that
If two figures are congruent, then its corresponding sides and its corresponding angles are congruent
In this problem
If
ABCD≅PQRS
then
<em>Corresponding angles</em>
∠A≅∠P
∠B≅∠Q
∠C≅∠R
∠D≅∠S
<em>Corresponding sides</em>
AB≅PQ
BC≅QR
CD≅RS
AD≅PS
To get the answer to this question simply add he numerators but keep the denominator the same which will give you 2/6 then you simplify the answer by 2/2 to get the simplified answer 1/3
