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.
Answer:
Step-by-step explanation:
Notice they both have the same slope of 3x so they are parallel, but different y intercepts. This means the lines never intersect and thus there are no solutions to the system of equations.
Answer:
My bid was $42 less than the winning bid.
Step-by-step explanation:
The winning bid is x.
$28 is 40% of x
0.4x = 28
x = 28/0.4
x = 70
The winning bid was $70.
$70 - $28 = $42
Answer: My bid was $42 less than the winning bid.
It can have however many x intercepts it wants,
<span>BUT, to be a function it must pass the vertical line test. </span>
<span>this means you have to look at the graph and see if a vertical line drawn anywhere hits the graph more than once. </span>
<span>if it hits it more than once, it is NOT a function.
</span>
An example is a polynomial function to the infinite degree. That is
f(x) = lim (n --> infinity) [ x^n]
but only 1 y intercept (vertical line test remember)
Step-by-step explanation:
The Circumference is:

Radius r is:

So,
