In calculus, we use derivatives to find the instantaneous rate of change at any point on a graph. To find the average rate of change, we just find the slope of the secant line that intercepts two points on the graph.
We find slope with the following equation:
In this case, we are looking for the slope from x = -1 to x = 1. We have both x values, so next we need the y values.
F(-1) = (-1)^2 - (-1) - 1 = 1
F(1) = (1)^2 - (1) - 1 = -1
Now plug in the x and y values to find the slope:
The answer is -1.
Start from the parent function
In the first case, you are computing
In the second case, you are computing
, you translate the function horizontally, units left if and units right if .
On the other hand, when you transform , you translate the function vertically, units up if and units down if .
So, the first function is the "original" parabola , translated units right and units up. Likewise, the second function is the "original" parabola , translated units left and units down.
So, the transformation from to is: go units to the left and units down
Attached is the solution, long division is hard to type out.
Hope it helps.
9*13=117
12*16=192
We increased three meters to both the length and width of the garden.
The domain and the range of the function are all possible values of the x and y, respectively, that function can take.
The range is given by:
The domain is given by: