If f(x)=2x-3 find yhe average gradient between x=-1 and x=-2
To find the average gradient between two points on a function, we need to calculate the difference in the function values at those points and divide it by the difference in the x-values.
Given that the function is f(x) = 2x - 3, we can substitute the x-values -1 and -2 into the function to find their corresponding y-values.
For x = -1:
f(-1) = 2(-1) - 3
= -2 - 3
= -5
For x = -2:
f(-2) = 2(-2) - 3
= -4 - 3
= -7
Now we have the points (-1, -5) and (-2, -7).
To find the average gradient, we calculate:
average gradient = (change in y) / (change in x)
Substituting the values:
average gradient = (-7 - (-5)) / (-2 - (-1))
= (-7 + 5) / (-2 + 1)
= -2 / -1
= 2
Therefore, the average gradient between x = -1 and x = -2 is 2.