Answer:
The correct answers are: 2x + 3y = 10 and 4x = 16.
Step-by-step explanation:
A function is a mathematical relationship between two variables, usually represented as an equation, in which each input value (in the domain of the function) is related to exactly one output value (in the range of the function).
The following equations represent functions:
2x + 3y = 10: This equation represents a function because for each value of x, there is exactly one corresponding value of y that satisfies the equation. For example, if x=1, then y=-4 satisfies the equation, and if x=2, then y=-2 satisfies the equation.
4x = 16: This equation also represents a function because for each value of x, there is exactly one corresponding value of y that satisfies the equation. In this case, y is not a variable, so the function is a special type of function known as a "constant function."
The following equations do not represent functions:
2x − 3 = 14: This equation does not represent a function because for each value of x, there are two possible values of y that satisfy the equation. For example, if x=1, then y=11 and y=17 both satisfy the equation.
3y = 18: This equation does not represent a function because it does not contain an x term. In order for an equation to represent a function, there must be a relationship between the two variables x and y.
14.6 = 2x: This equation does not represent a function because it does not contain a y term. In order for an equation to represent a function, there must be a relationship between the two variables x and y.
Therefore, the correct answers are: 2x + 3y = 10 and 4x = 16.
Answer:
2x + 3y = 10
3y = 18
Step-by-step explanation:
Given equations:
A function is a special type of relationship where each input (x-value) is related to exactly one output (y-value).
The given equations are all linear equations since the highest power of each variable is one.
A linear equation with only a x-variable is a vertical line: x = a.
A linear equation with only a y-variable is a horizonal line: y = a.
A vertical line is not a function as it has only one x-value yet infinite y-values, so each input is related to infinite outputs.
A horizontal line is a function as each x-value is related to one y-value, (albeit the same y-value).
Therefore, all the given equations are functions except the equations that contain only a variable in x.
Therefore, the equations that represent functions are:
