Answer:
(1/2, 6).
Step-by-step explanation:
Turning points in a graph may exist whenever the derivative equals 0. Hence, let’s differentiate and then solve our function.
We have:
Take the derivative of both sides with respect to x:
Simplify:
We will now set this equal to 0 and solve for x. Hence:
Hence, the graph turns at x=1/2. This is the x-coordinate.
Then it follows that the y-coordinate will be:
Hence, our coordinate Is (1/2, 6).
Answer:
The graph of the functions moves 4 units right, 3 units up stretches vertically by a factor of 3 and reflects horizontally.
Step-by-step explanation:
In order to find the function transformations, we must first determine what the base function is:
Next, we need to determine how the function is being affected by the transformations.
When the graph of the function moves 4 units right, we mus subtract 4 units from x, so the function looks like this then:
If we need to stretch it vertically by a factor of 3, we need to multiply the function by 3:
If we need to reflect it horizontally, then we turn the 3 into a negative so we get:
And finally, if we wanted to move the graph up by 3 units, then we need to add 3 units to the whole graph, so we get:
in the attached picture you will be able to see the graph of the base function with all the transformations.
