+25 1) Let f(x)={3xif x<3,3xif x≥3. Find f(2)+f(3)+f(4).
2) Let f(x)={−2xif x<0,x2if x≥0. Find the range of f(x) in interval notation.
3) Find the area of the region that lies below the graph of y = 3 - |x - 1| but above the -axis.
+9488 1)
f(x)={3xif x<3,3xif x≥3.
Let's find f(2)
2 < 3 so we use f(x) = 3x
f(2) = 3(2)
f(2) = 6
Let's find f(3)
3 ≥ 3 so we use f(x) = 3x
f(3) = 33
f(3) = 27
Let's find f(4)
4 ≥ 3 so we use f(x) = 3x
f(4) = . . .? Can you figure this one out?
+9488 2)
f(x)={−2xif x<0,x2if x≥0.
Let y = f(x) so we can say that...
The range includes the smallest possible y value to the biggest possible y value.
A graph might help:
The smallest possible y value is 0
There isn't a biggest possible y value because we can always find a bigger one, so we say it's ∞
So the range is [0, ∞)
