I don't understand the equation y = -4 (2) ^x

Question

I understand that it's an exponential equation, but I can't figure out the steps I should take in order to actually graph it. Do you first multiply the -4 by 2, then solve it as "y = -8^x"? Even then, I don't understand how to make that into a graph. This is how I'm trying to solve it:

y = -4 (2) ^x ---> y = -8 ^x

x | y

0 | -1

1 | -8

2 | -64

3 | -512

Even though this way of solving the equation makes sense to me, it does not match up with the graphs the internet and my calculator are pulling up. Help would be great!

Answer 1

Hey there Aubrey! Hopefully, I can clear up some confusion. When you have something like 2^x, the exponent is only attached to 2. That coefficient (the -4) isn't only multiplying the two like the situation of 2x, it's multiplying the whole thing of 2^x

Here's an example:

2^x

x | y

0 | 1

1 | 2

2 | 4 = 2*2

3 | 8 = 2*2*2

4 | 16 = 2*2*2*2

-4 * 2^x

So when x = 3

-4 * 2^3

-4 * 2 * 2 * 2

The Coefficient can't change or affect the 2^x because they have different exponential values, plus there is only one -4

Hopefully, this helped! A good reminder is to always put things connected to exponents in parenthesis! (EX: 4(x^2) or 3(3^x))