1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
melomori [17]
3 years ago
12

Find domain and range for f(x)=x^2-2x+2

Mathematics
1 answer:
mr_godi [17]3 years ago
5 0

Answer:

Domain: (-∞,∞) or  -∞ <x<∞

Range: [1,∞) or y\geq 1

Step-by-step explanation:

Given function:

f(x)=x^2-2x+2

To find range and domain of the function.

Solution:

The given function is a second degree function as the highest exponent of the variable is 2. Thus, it is a quadratic function.

For all quadratic functions the domain is a set of all real numbers. So, the domain can be given as: (-∞,∞) or  -∞ <x<∞

In order to find the range of the quadratic function, we will first determine if the function has a minimum point or the maximum point.

For a quadratic equation : ax^2+bx+c

1) If a>0 the function will have a minimum point.

2) If  a the function will have a maximum point.

For the given function: f(x)=x^2-2x+2

a=1 which is greater than 0, and hence it will have a minimum point.

To find the range we will find the coordinates of the minimum point or the vertex of the function.

The x-coordinate h of the vertex of a quadratic function is given by :

h=\frac{-b}{2a}

Thus, for the function:

h=\frac{-(-2)}{2(1)}

h=\frac{2}{2}  [Two negatives multiply to get a positive]

h=1

To find y-coordinate of the vertex can be found out by evaluating f(h).

k=f(h)

Thus, for the function:

k=f(1)=(1)^2-2(1)+2

k=f(1)=1-2+2

k=f(1)=1

Thus, the minimum point of the function is at (1,1).

thus, range of the function is:

[1,∞) or y\geq 1

You might be interested in
A classroom can accommodate less than 24 students.
Effectus [21]
The answer is c because it’s asking for less than so it goes left and the dot isn’t filled so it means less than
6 0
3 years ago
In a class there are 40 students 30 are boys and what is the percentage of girls ....​
Artyom0805 [142]

Answer:

25%

Step-by-step explanation:

Total= 40 students

boys +girls= 40

30 +girls= 40

number of girls

= 40 -30

= 10

Percentage of girls

=  \frac{10}{40}  \times 100\% \\ =  25\%

Alternatively,

percentage of girls

= 100% -(percentage of boys)

= 100\% - ( \frac{30}{40}  \times 100\%) \\  = 100\% - 75\% \\  = 25\%

6 0
2 years ago
Can someone please help me with math???
arlik [135]

Answers:

2x + 7

2x - 7 = 14

2 + 7

4 0
3 years ago
Answer this please please
zloy xaker [14]

Answer:

x is less than -3

Step-by-step explanation:

3x^2+9x<0

x^2+3x<0

x(x+3)<0

x+3<0

x<-3

6 0
2 years ago
Pls help! 16 points:)
kenny6666 [7]

Answer: 52 degrees

Step-by-step explanation:

most likley like if correct

7 0
2 years ago
Read 2 more answers
Other questions:
  • PLEASE ANSWER QUICK
    15·1 answer
  • A plumber charges 25$ for a service call plus 50$ per hour of service.write an equation for the cost,C,after h hours of service.
    8·1 answer
  • Can u explain when answering thanks !
    10·1 answer
  • (27 thousands 3 hundreds 5 ones) x 10= How many thousands are in your answer
    5·2 answers
  • Simplify to create an equivalent expression -5(3p+3)+9(-7+p)
    12·1 answer
  • What is 3/5 divided by 9/5?
    11·1 answer
  • A rectangle has a length of 28 in and a width of 3ft. what is the perimeter of the rectangle?
    10·1 answer
  • If a || b and _____, then a || c.
    12·1 answer
  • What is the equation of the line in point-slope form that has a slope of -3 and passes through the point (5, 9)?
    11·1 answer
  • 3. You and your friends were playing basketball last week. You were short a
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!