Given f’(x), where is f(x) increasing? Where is f(x) concave up?
1 answer:
You might be interested in
Multiplying the whole function by -1 reflects the function across the x axis
so f(x) to -f(x) would be a reflection across the x axis
multiplying the whole function by a fraction is a vertical transformation, if you multiply by a value x, such that 0<x<1, then it is a vertical shrink, if x>1, then it is a vertical stretch
so like f(x) to 2f(x) is a vertical stretch by a factor of 2
adding a value to the whole function moves it up by that number
ok
so
we have multiplied the whole thing by -1 and 1/2 and then added 2 to the whole function
that is a reflection across the x axis, a vertical shrink by a factor of 1/2, and translated up by 2 units in that order
so f(x) to -f(x) would be a reflection across the x axis
multiplying the whole function by a fraction is a vertical transformation, if you multiply by a value x, such that 0<x<1, then it is a vertical shrink, if x>1, then it is a vertical stretch
so like f(x) to 2f(x) is a vertical stretch by a factor of 2
adding a value to the whole function moves it up by that number
ok
so
we have multiplied the whole thing by -1 and 1/2 and then added 2 to the whole function
that is a reflection across the x axis, a vertical shrink by a factor of 1/2, and translated up by 2 units in that order