I need help with graphing log base of 2 (4-X)
I get confused with the shifting
I need help with graphing log base of 2 (4-X)
I get confused with the shifting
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
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 = log_{2}(4 - x) <==> 2^{y} = (4 - x)
2^{0} = 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} = 2^{2}
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.