Can somebody use a program to make this image clearer?? I also don't know how to graph log functions and I am disappointed in the instructor alot.
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Remember that log (a) is only defined if a is positive. So log (y2) is only defined if y2>=0. ie y>=2. That's why the calculator says what it does. So there will be no part of your graph under or on the line y=2.If you give the Yvalue a negative number, then the calculator will say "Not a number"
Can you post the exercise statement verbatim? In this graphing exercise, I'm not sure if y is the independent variable or the dependent variable. In the former, the yaxis is horizontal; in the latter, the xaxis is horizontal.... What am I doing wrong with my graphing???
log_{2}(y  2) is undefined (in the Real number system) for any value of y that's 2 or less.If you give the Yvalue a negative number, then the calculator will say "Not a number"
Remember that log (a) is only defined if a is nonnegative. So log (y2) is only defined if y2>0. ie y>2. That's why the calculator says what it does. So there will be no part of your graph under the line y=2.
You say: "What am I doing wrong with my graphing???"
If you are going to draw the graph by plotting points, you simply need a lot more points, and join them with a smooth curve not straight lines.
Try y= 2.5 y=2.1, y=2.01 for example.
You also say: "I am not going to put it in a form without the log." But that would be the best way to graph this question.
\(\displaystyle x=2*log_2{(y2)}\)
\(\displaystyle \frac{x}{2}= log_2{(y2)}\)
\(\displaystyle y2=2^{\frac{x}{2}}\)
\(\displaystyle y=2^{\frac{x}{2}}+2\)
Can you graph that exponential function either
1. by plotting points as before
OR even better (2) by considering transformations of the graph of \(\displaystyle y=2^x\) ?
Except (using your calculator) you didn't get the same answers.Besides you get the same answers anyway …
You can google for lessons, but the main part in solving the given equation for y is understanding how to switch between logarithmic and exponential form. That comes directly from the definition of logarithms. Logarithms are a special way of writing exponents.I don't know how to flip the variables around and end up with an exponential form ...
You have all of those backward. f(x) is the value of the function when evaluatedJeffM said:\(\displaystyle f(x) = log_{10}(x)\).
\(\displaystyle f(\ 2)= 0.01\)
\(\displaystyle f(\ 1)= 0.1\)
\(\displaystyle f(0) = 1.\)
\(\displaystyle f(0.5) \approx 3.2.\)
\(\displaystyle f(1) = 10.\)
\(\displaystyle f(1.125) \approx 13.3.\)
This is exactly what a graphing calculator does except with many more points.
I don't understand "log_{2} times y", but I do have some final comments on this exercise. In the op, you had made it sound like this was a graphing exercise. But, it's not. They gave you the graph.… instead of looking at it as x=2*log_{2}(y2), just look at it as x=log_{2} times y …
To ironsheep. Do you really read \(\displaystyle \log_2(y)\) as "log base 2 times y "?instead of looking at it as x =2 log(y2), just look at it as x = log subscript 2 times y. That would mean as you exchange 2 to the power of x = 2 (Y2). Y equals (2 to the power of x) plus 4 and all of that is divided by 2. Just have to make the formula look simpler, which will allow me to get rid of the log