SOLUTION: Graphs this following function. g(x)=-log(1/2)(x-1)

Question 382397: Graphs this following function.
g(x)=-log(1/2)(x-1)

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
To graph this we need a table of values. For a table of values you pick values for x and use the function to find the function's value for that x. Each pair of numbers represents a point on the graph. Plot these points. Keep finding and plotting points until you get an idea of what kind of curve is being formed. Then sketch in the rest of the curve.

There are a couple of ways to build this table of values:

Clever: Pick x values such that x-1 is a power of 1/2. These logarithms can be found "by hand". For example, if x = 3 then x-1 is 2 and since the base 1/2 logarithm of 2 would be -1. This gives us a point: (3, -1). Another example would be x = 2 making x-1 a 1. And since the logarithm will be 0. Our point: (2, 0).
Convert the base 1/2 logarithm to an expression of base 10 (or base e) logarithms so we can use our calculators. This conversion is done using the base conversion formula for logarithms:

Using this formula to convert your logarithm we get:

Since log(1/2) = -0.3010299956639812 this becomes:

(You probably want to round off that long decimal.) Now you can pick any number you want for x (as long as it is greater than 1). Then you can use your calculator to find the function's value for each x.

RELATED QUESTIONS
Use the given graphs of the function f (in blue) and g(in red) to find the following... (answered by ikleyn)

Perform the following function composition g(f(x)). * f(x) = x^2 - 1 g(x) = 1/x - 1... (answered by josgarithmetic)

g(x)=x^2+1 evaluate this function at... (answered by drk)

Evaluate the function at the indicated values g (x) = 1-x/1 + x g(2), g(-2),... (answered by Nate)

g(x) = log (base 1/3)... (answered by tommyt3rd)

Help me please. I need this by 2:50am eastern timezone. 1. Given the function g... (answered by jim_thompson5910)

Describe the transformation of f(x) represented by g(x). Then graph the function f(x)... (answered by MathLover1)

Look at this function: g(x)= x^3+x^2-x+1 What is the value of g(e)= ? Look at... (answered by algebrapro18)

let g(x) = 1/x^2 and h(x)= 1/((sqrt x )- 1) please determine the the following function (answered by jim_thompson5910)