Thread: Determining whether an equation defines a function of x?

How do i do that?

1) x^2 - y = 12

how do i determine whether it defines a function of x?

Defining that as a function of $\displaystyle x$ is equivalent to say "in terms of $\displaystyle x.$" Hence, isolate $\displaystyle y$ and you'll get a function in terms of $\displaystyle x.$ What's the name of that curve?

so i can substitue f(x) as y... OK!

ok i have another question...i have a few of these to do and they all look like their functions of x...i just rearranged the y so that its isolated...so since they all work, does that mean their all functions?

Originally Posted by realintegerz

ok i have another question...i have a few of these to do and they all look like their functions of x...i just rearranged the y so that its isolated...so since they all work, does that mean their all functions?

it depends on how the question was phrased.

it might mean you should solve for y and then say whether what you have is a function, or just note that anything that does not look like "y = something with x's in it" is not defined as a function of x. then there might be cases where you can't solve for y altogether, in which those are definitely not the functions you want