Question: The graph of [MATH]f(x) = log_2x[/MATH] has been transformed to [MATH]g(x) = alog_2x+k[/MATH]. The transformed image passed through the points (1/4, -9) and (16, -6). Determine the values of a and k.
I'm not entirely sure how to determine the values of a and k. My initial observation were that only the y values change and not the x values. So, I proceeded to find the parent points:
Transformed Point: (1/4, -9)
[MATH]y=log_2(1/4)[/MATH][MATH]2^y = 1/4[/MATH][MATH]ylog_2 = log(1/4)[/MATH][MATH]y=log(1/4)/log2[/MATH][MATH]y=-2[/MATH]Parent Point: (1/4, -2)
I then did the same thing for the other transformed point and got (16, 4) as the parent point.
As to what I do next, I have no idea. I'm not even necessarily sure if you're required to find the parent points, I just solved for them because it was the only thing I could think of.
What happens next after I find the parent points? Or what should I have done differently?
I'm not entirely sure how to determine the values of a and k. My initial observation were that only the y values change and not the x values. So, I proceeded to find the parent points:
Transformed Point: (1/4, -9)
[MATH]y=log_2(1/4)[/MATH][MATH]2^y = 1/4[/MATH][MATH]ylog_2 = log(1/4)[/MATH][MATH]y=log(1/4)/log2[/MATH][MATH]y=-2[/MATH]Parent Point: (1/4, -2)
I then did the same thing for the other transformed point and got (16, 4) as the parent point.
As to what I do next, I have no idea. I'm not even necessarily sure if you're required to find the parent points, I just solved for them because it was the only thing I could think of.
What happens next after I find the parent points? Or what should I have done differently?