How to graph 2 times 1/2 to the x power

Question

i know you can't physically graph this for me but I barely know how to do it with fractions and I'll appreciate if I get some help with this :)

Answer 1

The place to start is where the power (x in this case) is 0.  Any non-zero number raised to the power of 0 is 1, which is then multiplied by 2 in this function.  Therefore, your first point is (0,2).

 

For each value of x greater than zero, you'll be multiplying the result by 1/2.  1/2 to the 1st power is 1/2.  To the 2nd power, it's 1/4.  To the 3rd power, it's 1/8.  This should help you figure out the shape of the graph in the positive direction.  (Just don't forget to multiply each value by 2!)

 

Now, for values of x less than zero, you'll be dividing the result by 1/2... which is the same as multiplying by 2 (the reciprocal of 1/2).  1/2 to the -1 power is 2.  1/2 to the -2 power is 4.  1/2 to the -3 power is 1/8.  This should help you figure out the shape of the graph in the negative direction.  (Again, don't forget to multiple each value by 2...)

 

I hope this helps!

 

Jeff