Explain Square Root Function

Question

Explain how negative signs can affect the direction of a graph of a square root function. Talk about starting points, direction and end behavior. You have 4 different possibilities (zero negative signs, one negative sign in one of two places, or two negative signs) Make sure you use common mathematical language and examples to explain your answer. Please Answer.

Answer 1

For problems like this, I always recommend using the Desmos (or some other) graphing utility so you can visualize the situation. The problem asks you to look at four possibilities, which in their simplest form would be

√x

-√x

√-x

and

-√-x

Begin your discussion by explaining why the √x function cannot have any negative values of x in its domain. I'm sure you're familiar with the idea that square roots of negative numbers are undefined in real numbers.

Note that there are also no negative y values generated for this function. Why? Well, clearly the square root of any positive number is another positive number.

Answer the same questions for each of the other possibilities, and you're all set.

Best wishes!