The following information is given,
f(x) = 2+x x<(less than or equal to) -3
f(x) = x^2 x > -3 , x < 1
f(x) = 6 1 < (less than or equal to) x
I graphed it, but i don't know how to find the domain and range.
The domain is the allowed values of x (excluding the non allowed).
The range is the value of f(x), which you compute from x.
I will be happy to critique your thinking.
for f(x) = 2+x : Domain: (negative infinity to -3]
Range: (-infinity to -1]
f(x) = x^2 : Domain: (-3,-1)
Range: (9,1)
f(x) = 6 : Domain: [-3,-1]
Range: [6]
i don't know how to put them all together though. is this right?
on the second, the domain does not include -1 nor -3, you have to be careful on the non-included points. Same on the range, you can list it as 9-e,1+e where e is epsilion.
For an all together ,
domain: neginf to +inf
range: neginf to 9, excluding -1+e to 1 (check that).
There is an assortment of the ways you can describe this.
That assortment could include notations such as set builder and interval.
To find the domain and range of a function, you need to consider all the possible x-values (the domain) and the corresponding y-values (the range) that the function can take.
Given the function f(x) with the given conditions:
1. f(x) = 2 + x when x ≤ -3
2. f(x) = x^2 when -3 < x < 1
3. f(x) = 6 when 1 ≤ x
To determine the domain:
1. For the first part, f(x) = 2 + x, it is valid for all x-values less than or equal to -3.
So, the domain for this part is x ≤ -3.
2. For the second part, f(x) = x^2, it is valid for all x-values between -3 and 1, excluding -3 and 1.
So, the domain for this part is -3 < x < 1.
3. For the third part, f(x) = 6, it is valid for all x-values greater than 1.
So, the domain for this part is x > 1.
Combining all the valid domains:
The domain for the function f(x) is x ≤ -3, -3 < x < 1, and x > 1.
To determine the range:
For the domain values given, let's analyze each part separately:
1. For the first part, f(x) = 2 + x, the range can be any value since there is no restriction on the function for this part.
2. For the second part, f(x) = x^2, as x varies between -3 and 1, the values of f(x) will depend on the x-values. Since x^2 is always positive or zero, the range for this part is greater than or equal to 0.
3. For the third part, f(x) = 6, the function f(x) is always equal to 6 when x is greater than 1. Thus, the range for this part is 6.
Combining all the valid ranges:
The range for the function f(x) is all real numbers greater than or equal to 0, including 6.
So, the domain is x ≤ -3, -3 < x < 1, and x > 1, and the range is all real numbers greater than or equal to 0, including 6.