Question

Look at picture above. I need help to understand it. I’m not sure how to do it. And I can’t continue until I get this answer. Thank you

Answer 1

1. If you have a negative base and you try to take the square root of it you get an imaginary number.

2. To get the second point, raising 1 to x will always get you 1 and raising 0 to x will always get you 0.

Explanation:

For example if you have the square root of -64, you get +8i and -8i since you're taking the square root. This means that there are no real roots. They're imaginary.

y = 1^x. if we chose the values: 1, 2, 3, 4 to be our x we will always end up with 1 as our answer. If you graph this, you will see a straight horizontal line at y = 1.

This is why it's not an exponential function. It doesn't behave the same way other exponential functions do. You can have a much better understanding if you use a graphing calculator to actually how it looks (try desmos online if you don't have a gc).

Now y = 0^x will also always result in an answer of 0. Take x as 1, 2, 3, 4. 0*0 = 0. 0 * 0 * 0 = 0. I think you get the point. Exponential functions show exponential growth while y = 1^x and y = 0^x are straight horizontal lines, not exponential functions.

Answer 2

1. Negative values of b would mean that y can fluctuate between a positive and negative answer depending on what is used for x. In simpler terms, if b < 0, y can be both less than and greater than 0. If b > 0, y can only be greater than 0. This means that only functions where b > 0 can be defined. You would not want to use negative values of b because the answer will not always be a natural number.

2. You cannot consider y = 1^x or y = 0^x to be exponential functions because, while they do utilize an exponent, they do not create exponential growth. 1 multiplied by itself, no matter how many times, will always result in 1. Similarly, 0 multiplied by itself will always result in 0. Therefore, no exponential growth is occurring in either of those equations. (I think this answer is more up to interpretation. I'm sure an argument can be made for those two equations to be considered exponential functions because they have exponents in them. The important thing to recognize here is that no growth occurs with either of them. Therefore, they are different from other "exponential functions").