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# Nonlinear equation graphs — Harder example

Watch Sal work through a harder Nonlinear equation graphs problem.

## Want to join the conversation?

• Why are the harder examples always easier than the practice problems?
• yeah ive struggled with the fact that the"harder" examples is just one example and there are multiple kinds of problems it does not show you how to solve
• Is there an algebraic way of solving this kind of problem? I'm aware that you can simply plug in the possible values for the variables to reach an answer, but I'm trying to fully understand the topic as well.

EDIT: I've looked up ways to solve this, and it seems like you have to graph each inequality. Are graphing and plugging in points the only two options when trying to solve this problem?
• Unfortunately, I don't think so. The problem is that the `x` is in the exponent section, and although it might be solved using logarithms or other advanced math, it's probably easier and faster to just plug in the numbers.
• Is there another way to find out the answer other than plugging in random numbers?
• I'd say plugging in random numbers is the most accurate solution you could do here, because just doing brute force math without much logic and reasoning lowers the chance for you to make a mistake. However, you're right, you can solve this problem another, faster way.

You're asked to find the graph of the negative of the function you're given. Putting a negative on a function like that basically means you're flipping it about the x-axis. So if we know the shape of the original function, we can just flip it horizontally and get our answer from there.
The function's equation looks exponential. The value of the constant being raised to a variable power is 1/3 here, which tells us that we're looking at exponential decay here and not growth (it's less than 1). We also have a minus 1 tacked onto the end. The minus 1 moves the whole function down by 1. So normally, the function would start at infinity, and decay exponentially until it hits an asymptote of -1.
We then flip this in our heads (or draw a sketch on the paper and flip that). Now our function has an asymptote at positive 1, and decays exponentially but in the opposite direction, getting more positive by decreasing amounts instead of getting more negative in decreasing amounts. Choice D) is the only one that matches this.
• the harder example is easier than the basic one
• What if x goes -1......-2......-3.....-4 and so on?
• When you say a function increases, then you're assuming x is increasing unless otherwise specified.
• lets go October sat here baby!! Need a thick 800 math score
• I need all of you to solve this: 2 - X = X^2 + 4
(1 vote)
• 2 - x = x^2 + 4
x^2 + 4 + x - 2 = 0
x^2 + x + 2 = 0
(x + 2)(x - 1) = 0
x = -2 and 1