How would you tell if an equation is a funtion or not. I know that it has to have only one y-value for every x...but how do you identify this in an equation (rather than a graph)

Question

How would you tell if an equation is a funtion or not. I know that it has to have only one y-value for every x...but how do you identify this in an equation (rather than a graph)

ie. y=1/2x-7 (how do i tell if this is a funtion or not)?
Any help would be much appreciated :)

Answer 1

when dealing with linear functions, the general formula is y= mx + c..where m is the gradient and c is the y-intercept. To find the value of x simply make y = to zero.hence the equation(y=1/2-7) is a linear function because if substituted in the general formula,1/2 would be the gradient(since it is the value/coefficient of x),, c=-7 and x=-1.

Answer 2

Please use parentheses where needed for clarity. I don't know if that is

1/(2x-7) or (x/2) -7 or (1/2x) -7

In each case, y is clearly a function of x because there is one and only one y for each x. (Except possibly where a denominator vanishes)

Answer 3

To determine whether an equation represents a function, you need to check if there is more than one y-value for any given x-value. Here's how you can identify whether the equation y = (1/2)x - 7 represents a function:

1. Understanding the equation: The equation is in the form y = mx + b, where m represents the slope (in this case, 1/2) and b represents the y-intercept (in this case, -7).

2. Confirming the rule: A function must have only one y-value for each x-value. In other words, for every x-value you plug into the equation, there should be only one corresponding y-value.

3. Check multiple x-values: Select two or more x-values and calculate the corresponding y-values. For example, let's take x = 1 and x = 2:

For x = 1:
y = (1/2)(1) - 7
y = 1/2 - 7
y = -13/2

For x = 2:
y = (1/2)(2) - 7
y = 1 - 7
y = -6

4. Analyzing the results: By analyzing the calculated y-values, we can see that for each x-value we plugged in, there is only one y-value. In this case, -13/2 and -6 are unique y-values for each x-value, so the equation y = (1/2)x - 7 is indeed a function since it satisfies the one-to-one mapping rule.

To summarize, you can determine whether an equation represents a function by checking if there is only one y-value for every x-value. By substituting different x-values into the equation and examining the resulting y-values, you can confirm if the equation satisfies this condition.

How would you tell if an equation is a funtion or not. I know that it has to have only one y-value for every x...but how do you identify this in an equation (rather than a graph)

Please use parentheses where needed for clarity. I don't know if that is

thanks :)

To determine whether an equation represents a function, you need to check if there is more than one y-value for any given x-value. Here's how you can identify whether the equation y = (1/2)x - 7 represents a function: