If the point (40,3) is on the graph of y=f(x), what point must be on the graph of y=8f(8x)?
The point (?,?) must be on the new graph.
well,
f(40) = 3
8f(8x) = 8f(320)
Unfortunately, know f(40) tells us nothing about f(320).
I think you have left out something.
Describe the effect that the transformations y=8f(8x) have on the graph of y=f(x).
shrink horizontally by a factor of 8
stretch vertically by a factor of 8
If you think on it a bit, you should see why. Try using some online grapher to experiment.
I think you are looking for (5,24).
An interesting way to pose the problem.
To find the point that must be on the graph of y=8f(8x), we can start by substituting the given point (40,3) into the equation.
Given:
y = f(x) (1)
y = 8f(8x) (2)
Point on graph of y=f(x): (40,3)
Substituting (40,3) into equation (1):
3 = f(40)
Now, let's substitute the value of 40 into equation (2):
y = 8f(8 * 40)
y = 8f(320)
Since we know that 3 = f(40), we can substitute this value into the equation:
y = 8(3)
y = 24
Therefore, the point on the new graph is (320, 24).