Y=mx
m=amount of time per day studied
y=time
x=number of days
we have
60=m(4)
divide by 4
15=m
y=15x
Expanding
-3h-15+2=4h+24-9
-3h-4h=24-9-2+15
-7h=28
h=4
In both cases you may well benefit from graphing the functions.
Do you recognize f(x) = (x + 1)^2 - 1 as a quadratic function, whose graph is that of a parabola that opens up? By comparing this to y = a(x-h)^2 + k, we see that a=1, h= -1 and k = -1. The vertex is at (h,k), which here is the point (-1, -1). This is the minimum value of the function. Thus, the range of this function is [-1, infinity).
Now for the function f(x) = 7x - 11: This is a linear function whose graph is (surprise!) a straight line. When x increases, y increases, without limits to either. Similarly, when x decreases, y decreases.
Thus the range includes all real numbers: (-infinity, infinity).
