Domain is the numbers you can use
see we have rom x<-3 and x≥-3
therefor it is all real numbers for the domain
domain=all real numbers
and the range is the output
for all numbers less than -3, we have x+4, so -10+3=-7, so it extends infinetely in negative direction
and for x^2+6, you start with -3 which ends with (-3)^2+6=9+6=13, after that it gets bigger
so therefor the range is
from -∞ to -7, not including -7 and from 13 to positive infinity
in interval notation
(-∞,-7)U[13,∞)
domain=all real number
range=(-∞,-7)U[13,∞) or all real numbers except all numbers c, such that -7≤c<13
Only f(x) as that is the only equation which has no end in the graph shown.
Step-by-step answer:
Given:
Circle C1: x^2+y^2 = 45
Line L1: -3x+y=15
Need to find the points of intersection.
Solution:
basically we need to solve for the roots of equations C1 and L1.
Here, we can use substitution of L1 into C1.
Rewrite L1 as : y=3x+15
substitute into C1:
x^2+(3x+15)^2 = 45
Expand
x^2 + 9x^2+90x+225 = 45
Rearrange terms:
10x^2+90x+180 = 0
Simplify
x^2+9x+18 = 0
Factor
(x+6)(x+3) = 0
so
x=-6 or x=-3
Back-substitute x into L1 to calculate y:
x=-6, y=3*x+15 = 3(-6)+15 = -3 => (-6,-3)
x=-3, y=3*x+15 = 3(-3) + 15 = 6 => (-3, 6)
Therefore the intersection points are (-6,-3) and (-3,6)
Check using equation C1:
(-6)^2+(-3)^2 = 36+9 = 45 ok
(-3)^2+(6)^2 = 9 + 36 = 45 ok
Check using equation L1:
Point (-6,-3) : y = 3x+15 = 3(-6) +15 = -3 ok
Point (-3,6) : y = 3x+15 = 3(-3)+15 = 6 ok.
A reciprocal is the inverse of a number. if you are given a whole number such as 2 or 3 or 4 or 5... etc. then you flip the number by putting a 1 as the numerator. so the reciprocal of 2 is 1/2 and for 3 it is 1/3 and 4 is 1/4... and so on...
first put your decimal in fraction form
2.5 = 2 and 5/10
= 2 and 1/2
= 5/2 ---> 2/5 (0.4) is the reciprocal of 2.5
