domain = set of all possible values of x
range = set of all possible values of y
(1) y = sqrt(x-3)
note that the term inside the sqrt can be zero but cannot be negative, for it will become imaginary. thus,
Domain: x must be greater than or equal to 3.
also, y can be zero (if x=3) but can never be negative since sqrt of any positive real number is always positive, thus,
Range: y must be greater than or equal to 0.
(2) y = 3x + 5
this is an equation of a line, and note that there is neither restriction in both x and y, thus,
Domain: x can be all real numbers
Range: y can be all real numbers
(3) y = 2/(x-7)
note that denominators cannot be 0, thus,
Domain: x can be all real numbers except 7.
for the range, observe that y cannot be equal to zero, because, if so,
0 = 2/(x-7) , then cross-multiplying,
0 = 2 , which is wrong, thus
Range: y is all real numbers except 0
(4) y = 2 + sqrt(x)
note that this is almost similar to #1, except that there is +2. therefore,
Domain: x must be greater than or equal to zero.
for the range, the minimum possible value of x is zero, but because there is +2,
Range: y must be greater than or equal to 2.
hope this helps~ :D
Answer this Question
algebra - Graph the following function using the technique of shifting, ...
Domain- Interval Notation - Domain of g(x) g(x)= sqrt(3-(sqrt(25-x^2)) I got -5...
calculus - find the domain of the following function. State your answer in ...
graphing - (0,-2)is the vertex- what is the domain and range??? State the domain...
maths - what is the largest domain of the following functions f(x)=3x-5 f(x)=...
Algebra - Ok I got another one I can figure out The one-to-one function f is ...
Algebra - Hello again, I am now working on trying to find the relation of x = 1...
is this correct?- math - find the domain of the real valued function; f(x) = ...
Algebra-I'm still stuck - The one-to-one function f is defined by f(x)=(4x-1)/(x...
math - questions involving domain and range... 1. Find the domain of the ...