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).
1. 9/10 + 7/9 = 81/90 + 70/90 = 151/90 = 1 61/90
2. 1/2-3/11 = 11/22-6/22 = 5/22
3. 2/5-1/15 = 6/15-1/15 = 5/15 =1/3
Answer:
1/25
Step-by-step explanation:
f(x)=5^x
Let x = -2
f(-2)=5^-2
We know that a^-b = 1/a^b
= 1/5^2
= 1/25
Answer:
The change received by Judy is $ 2.69.
Step-by-step explanation:
Bill paid = $ 10
Cost of binder = $ 1.38
Cost of pack of pencils = $ 2.05
Cost of box of erasers = $ 3.88
Total cost of the school supplies = $ 1.38 + $ 2.05 + $ 3.88 = $ 7.31
The amount of change Judy received = $ 10 - $ 7.31 = $ 2.69
