(2,-7) is a point on the graph of y=f(x) . Find the corresponding point on the graph of y= 3f(5(x-1)+1 .
An object travelling in a straight line away from a motion sensor at a constant rate moves from 4 m away to 16 m away between t = 1 s and t = 6 s. Describe the segment corresponding to this walk on the speed versus time graph.
To find the corresponding point on the graph of y = 3f(5(x-1)+1) when (2,-7) is a point on the graph of y = f(x), we need to substitute the x-coordinate of (2,-7) into the equation y = 3f(5(x-1)+1) and calculate the corresponding y-coordinate.
Given point on the graph of f(x):
x = 2
y = -7
Substituting x = 2 into y = 3f(5(x-1)+1):
y = 3f(5(2-1)+1)
Simplifying the expression inside the parentheses:
y = 3f(5(1)+1)
y = 3f(5+1)
y = 3f(6)
So, to find the corresponding point on the graph of y = 3f(5(x-1)+1) for (2,-7), we need to find f(6).
To find the corresponding point on the graph of y = 3f(5(x-1)+1), we need to substitute the x-coordinate (2) into the equation and calculate the corresponding y-coordinate.
First, let's simplify the expression inside the function f:
5(x-1) + 1
= 5 * (2-1) + 1
= 5 + 1
= 6
Now, substituting this value (6) into the equation, we have:
y = 3f(6)
Since (2,-7) is a point on the graph of y = f(x), it means that when x = 2, y = -7. So, f(2) = -7.
Now, substitute f(2) = -7 into the equation:
y = 3f(6)
= 3 * f(6)
= 3 * ???
Since we don't know the value of f(6), we cannot determine the corresponding point precisely. The corresponding point on the graph of y = 3f(5(x-1)+1) when x = 2 will depend on the specific function f(x). You would need to know the equation or have additional information about the function f(x) to calculate the value of f(6) and determine the corresponding point accurately.