Assume that f(3)=4. Name a point that must be on the graph of y=1/2f(x/2).
if x = 6
then f(x/2) = f(3) = 4
y = 4/2 = 2
(6,2)
To find a point that must be on the graph of the function y = 1/2f(x/2), we can use the given information that f(3) = 4.
We'll start by substituting x/2 into the equation f(x/2) to get the corresponding y-value.
f(x/2) = f(3/2) [Substituting x = 3 into x/2]
Now, since we know that f(3) = 4, we can substitute this value into f(x/2):
f(3/2) = 4
Next, we multiply the equation by 1/2 to obtain y:
y = 1/2 * f(3/2)
y = 1/2 * 4
y = 2
Therefore, the point (3/2, 2) must be on the graph of y = 1/2f(x/2) since the value of y for x = 3/2 is 2.