SOLUTION: What is the DOMAIN and RANGE for the following equations:
1) y = 3x - 4
2) y = -2x^2 + 2
3) y = x^3
I know how to graph I understand all that but I don'T know how to deter
Algebra ->
Graphs
-> SOLUTION: What is the DOMAIN and RANGE for the following equations:
1) y = 3x - 4
2) y = -2x^2 + 2
3) y = x^3
I know how to graph I understand all that but I don'T know how to deter
Log On
Question 15120: What is the DOMAIN and RANGE for the following equations:
1) y = 3x - 4
2) y = -2x^2 + 2
3) y = x^3
I know how to graph I understand all that but I don'T know how to determine the range and domain, are they looking for number pairs????
Thanks Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website! in these equations or functions as we call them you know that x is called the independent variable and y the dependent variable. that is we give different values to x and find the corresponding values of y.that is how you draw the graphs of the functions .
now to start with domain is the set of all values x can take and range is the corresponding set of values y can take .
what do we mean by the set of values x can take .As you know certain operations are prohibited or meaning less in maths.like division by zero.so if we have a function y=1/x , we say x can take any value except zero.so domain of x is all real numbers except zero . similarly if y= square root of x ,then domain is ... x can take all real non negative numbers.x cannot be negative as square root of negative number does not exist.
after determining the domain ,we find the set of corresponding values of y and call it the range of y.clear ?
now y=3*x-4 .. as there are no problem areas like division by x or squareroot of x etc..we can conclude that domain of x is all real numbers and range of y is also all real numbers
now y = -2x^2 + 2...domain of x is all real numbers as above.but as far as range is concerned we see that ...since square of x is always positive,its minimum value can be 0.hence -(square of x) has a maximum value of 0.hence has a maximum value of 1. hence y has a maximum value of 2 . hence range of y is all real numbers less than or equal to 2.you can check this from your graph too. you will find that as x changes from -infinity to +infinity , y changes from +2 to -infinity.
y = x^3...you can see here domain and range are set of all real numbers.
