how do you graph log base of 2(4-X)

Question

I need help with graphing log base of 2 (4-X)

I get confused with the shifting

Answer 1

Graph y1 = log[2] x

Flip it about y-axis to get y2 = log[2] (-x)

Shift it to the right by 4 units to get y3 = log[2] (4-x) <==Answer

Answer 2

You can certainly create a t-chart and evaluate the function for various x-values. However, to simply sketch the graph, we need some intercepts and an understanding of the graph's behavior via asymptotes.  

Firstly, we should understand the function is asymptotic at x = 4, since the log(0) = inf.

We can also understand that the behavior of the function is opposite of its parent function, log(x), since we effectively have log(-x). Therefore, we should understand that the function decreases from the left, and falls asymptotically at x = 4. Now we just need the intercepts.

The x-intercept is the value of x when y = 0. To figure this out, it's helpful to rearrange the equation in a different form.

y = log₂(4 - x) <==> 2^y = (4 - x)

2⁰ = 4 - x

1 = 4 - x

x = 3

Now for the y-intercept. Sub in zero for x and solve for y.

2^y = 4 - 0

2^y = 2²

Therefore, y = 2

Plot a vertical dashed line at x = 4, plot your intercepts and sketch the graph, understanding that the value of the function falls from left to right. Develop a t-chart if you want to fill in any other values.