How to graph 1/4 to the x+2 power

Question

i know you can't physically graph this for me but please tell me how to get the 5 points in order for me to graph it because I barely know how to do it with fractions and thank you:)

Answer 1

The first rule (I call this the most important thing that they didn't teach you in grade school math) is that fractions and division are the same thing, so 1/4 = 1 divided by four.  1/4 x 1/4 = 1 divided by 4 times 1 divided by 4, so look at that and you see 1 x 1 and divided by 4 divided by 4.  Dividing by 4 twice is the same as dividing by 16m, so 1/4 x 1/4  = 1/16.  This is the reason for the top times top and bottom times bottom rule for fractions. 

 

Therefore (1/4)^1 = 1/4, (1/4)^2 = 1/16, (1/4)^3 = 1/64, and so on.

 

Now use (1/4)^0 = 1 because anything to the zero power is one. 

 

And a negative exponent gives a reciprocal, so (1/4)^-1 = 4/1 = 4, (1/4)^-2 = 16/1 = 16. 

 

Now you can graph convenient points.  I mean by this ones that give small exponents.  For x = -1, x+2 = +1, and you have (1/4)^1 = 1/4, and you can graph a point.  Notice that negative exponents give high numbers and positive exponents give low numbers, so this is what is called an exponential decay, exponential because the variable in your function is in the exponent, and decay because things get smaller as x gets larger.