What is the range of the function y = x2 + 1?

Domain:  

x  ∈ R  or  x ∣ ( − ∞ ,

Range :  y ≥ 1  or  y ∣ [ 1 , ∞ ) .

Step-by-step explanation:

y

=

x

2

+

1

 , Domain : Possible input value of  

x

is

any real value . Therefore Domain:  

x

∈

R

or

x

∣

(

−

∞

,

∞

)

.

Range:  

y

=

x

2

+

1

or

y

=

(

x

−

0

)

2

+

1

. Comparing with vertex

form of equation  

f

(

x

)

=

a

(

x

−

h

)

2

+

k

;

(

h

,

k

)

being vertex

we find here  

h

=

0

,

k

=

1

,

a

=

1

∴

Vertex is at  

(

0

,

1

)

Since  

a

is positive the parabola opens upward and

vertex is the minimum point  

x

=

0

,

y

=

1

So range is  

y

≥

1

or

y

∣

[

1

,

∞

)

.

Domain:  

x

∈

R

or

x

∣

(

−

∞

,

∞

)

Range :  

y

≥

1

or

y

∣

[

1

,

∞

)

.

graph{x^2+1 [-10, 10, -5, 5]}

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

college