Can someone help me with my trig homework?

Question

I need to find the domain and range of this function: y = 3(x +1)^2 -5.

Are the domain and range all real numbers? And I do pay attention in school -- I just want to check my homework!

Answer 1

The domain is the set of all real numbers.
The range is the set of all real numbers greater than or equal
to -5.

Answer 2

The domain is simply all of the numbers that can be substituted for x. There is usually a restriction on x if it is in the denominator of a fraction, has a negative exponent, or is under a radical symbol. Since none of these cases applies to your function, the domain is from negative infinity to positive infinity

The range is a little bit more tricky. The range is all of the numbers that can be substituted for y. Notice that the graph of the function is a parabola. Since the x-term is positive, the graph looks like a smile. So, the ends of the parabola are going towards positive infinity. We will need this in a bit. Now we need to find the vertex of the parabola. Since we are only concerned about y-values, we only need the y-coordinate of the vertex. To find the vertex, we need to simplify the equation:

y = 3(x+1)^2 - 5
y = 3(x^2 + 2x +1) - 5
y = 3x^2 + 6x + 3 - 5
y = 3x^2 + 6x - 2

Now, the function is in the form y = Ax^2 + Bx + C. In your case, A = 3, B = 6, and C = -2. The y-coordinate of the function can be found with the following formula:

C - (B^2 / 4A)
= (-2) - (6^2 / 4*3)
= (-2) - (36 / 12)
= -2 - 3
= -5

Thus, the y-coordinate of the vertex of your function is -5. Hence, the range is from -5 (included) to positive infinity.

So,
domain: (negative infinity, positive infinity)
range: [-5, positive infinity)
(Sorry, I don't know how to put in the infinity symbol here.)

Answer 3

Domain is unlimited you can use any x in this function. it means Domain is :
x < 0
x = 0
x > 0
now Range
y = 3(x +1)^2 -5
y=3 ( x^2 + 1 + 2x) -5 = 3x^2 + 3+ 6x - 5 = 3x^2 + 6x - 2
if y= 0 then ;
3x^2 + 6x - 2=0
if a= +3 and b= +6 and c= -2 so we have:

Delta = b^2 - 4ac = 6^2 - 4* 3* -2 = 36 +24 = 60
Delta = 60

X1 = (-b + sqrt ( delta))/ 2a = -6 + sqrt (60) / 6 ~ + 0.29
x2 = (-b - sqrt ( delta))/ 2a = -6 - sqrt (60) / 6 ~ - 0.29

y1= 3(+ 0.29 +1)^2 -5= - 0.0077
y2 = 3(- 0.29 +1)^2 -5 = - 3.4877

so you Range is all the numbers between y1 and y 2 it means:
- 3.4877 <= y <= - 0.0077

Answer 4

substitute all the x and look for the value of y. all the domain are the values of x and all the ranges are the values of y.

Answer 5

go to your teacher and ask him to help you and oh! pay attention in school

Answer 6

STUDY and find your own answers,or call your math teacher!