The domain of the function refers to the complete set of possible values of the independent variable or the set of all possible values for x which will make the function work, and will derive real values for y.
Examples:
In {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}, the domains are 2, 4, 3, 6, 2.
In y = 2x - 3, the domains are the values of x that will make this equation true.
Range:
The range of the function refers to the complete set of all possible resulting values of the dependent variable such as y after replacing the domain.
Examples:
In {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}, the ranges are -3, 6, -1, 6, 3.
In y = 2x - 3, the ranges are the values of y that will make this equation true.
Sample Problems:
Find the x and y values that will make the equation: y = 2x - 3 possible.
Solve for x and y in the equation: x² - 1 = y.
Solutions 1:
Given: y = 2x - 3
Write the equation in standard form: -2x + y = -3.
Remove the negative value for x by multiplying both sides of the equation to -1 such that, -1[-2x + y = -3]-1 which is 2x - y = 3.
Solve for y in terms of x using x = 0. Then, -y = -2x + 3. Replacing x with 0 then, -y = -2(0) + 3.
Simplifying the equation it will give -y = 3.
Remove the negative value for y by dividing both sides of equation with -1 which is the numerical coefficient of y then, -y/-1 = 3/-1. Therefore, y = -3 when x = 0.
Solutions 2:
Given: x² - 1 = y
Write the equation in standard form: x² - y = 1.
Solve for y in terms of x using x = 0. Then, -y = -x² + 1. Replacing x with 0 then, -y = -(0)² + 1.
Simplifying the equation it will give -y = 1.
Remove the negative value for y by dividing both sides of equation with -1 which is the numerical coefficient of y then, -y/-1 = 1/-1. Therefore, y = -1 when x = 0.
The domain of the function refers to the complete set of possible values of the independent variable or the set of all possible values for x which will make the function work, and will derive real values for y.
Examples:
In {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}, the domains are 2, 4, 3, 6, 2.
In y = 2x - 3, the domains are the values of x that will make this equation true.
Range:
The range of the function refers to the complete set of all possible resulting values of the dependent variable such as y after replacing the domain.
Examples:
In {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}, the ranges are -3, 6, -1, 6, 3.
In y = 2x - 3, the ranges are the values of y that will make this equation true.
Sample Problems:
Find the x and y values that will make the equation: y = 2x - 3 possible.
Solve for x and y in the equation: x² - 1 = y.
Solutions 1:
Given: y = 2x - 3
Write the equation in standard form: -2x + y = -3.
Remove the negative value for x by multiplying both sides of the equation to -1 such that, -1[-2x + y = -3]-1 which is 2x - y = 3.
Solve for y in terms of x using x = 0. Then, -y = -2x + 3. Replacing x with 0 then, -y = -2(0) + 3.
Simplifying the equation it will give -y = 3.
Remove the negative value for y by dividing both sides of equation with -1 which is the numerical coefficient of y then, -y/-1 = 3/-1. Therefore, y = -3 when x = 0.
Solutions 2:
Given: x² - 1 = y
Write the equation in standard form: x² - y = 1.
Solve for y in terms of x using x = 0. Then, -y = -x² + 1. Replacing x with 0 then, -y = -(0)² + 1.
Simplifying the equation it will give -y = 1.
Remove the negative value for y by dividing both sides of equation with -1 which is the numerical coefficient of y then, -y/-1 = 1/-1. Therefore, y = -1 when x = 0.
Answers & Comments
Verified answer
Domain and Range of Functions:
Domain:
The domain of the function refers to the complete set of possible values of the independent variable or the set of all possible values for x which will make the function work, and will derive real values for y.
Examples:
Range:
The range of the function refers to the complete set of all possible resulting values of the dependent variable such as y after replacing the domain.
Examples:
Sample Problems:
Solutions 1:
Solutions 2:
Definitions of Range and Domain: brainly.ph/question/42072
Domain and Range of Functions:
Domain:
The domain of the function refers to the complete set of possible values of the independent variable or the set of all possible values for x which will make the function work, and will derive real values for y.
Examples:
In {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}, the domains are 2, 4, 3, 6, 2.
In y = 2x - 3, the domains are the values of x that will make this equation true.
Range:
The range of the function refers to the complete set of all possible resulting values of the dependent variable such as y after replacing the domain.
Examples:
In {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}, the ranges are -3, 6, -1, 6, 3.
In y = 2x - 3, the ranges are the values of y that will make this equation true.
Sample Problems:
Find the x and y values that will make the equation: y = 2x - 3 possible.
Solve for x and y in the equation: x² - 1 = y.
Solutions 1:
Given: y = 2x - 3
Write the equation in standard form: -2x + y = -3.
Remove the negative value for x by multiplying both sides of the equation to -1 such that, -1[-2x + y = -3]-1 which is 2x - y = 3.
Solve for y in terms of x using x = 0. Then, -y = -2x + 3. Replacing x with 0 then, -y = -2(0) + 3.
Simplifying the equation it will give -y = 3.
Remove the negative value for y by dividing both sides of equation with -1 which is the numerical coefficient of y then, -y/-1 = 3/-1. Therefore, y = -3 when x = 0.
Solutions 2:
Given: x² - 1 = y
Write the equation in standard form: x² - y = 1.
Solve for y in terms of x using x = 0. Then, -y = -x² + 1. Replacing x with 0 then, -y = -(0)² + 1.
Simplifying the equation it will give -y = 1.
Remove the negative value for y by dividing both sides of equation with -1 which is the numerical coefficient of y then, -y/-1 = 1/-1. Therefore, y = -1 when x = 0.