Range is the value of y
f(x)=-x²+5
when x=-1, f(x)=-(-1)²+5=4
when x=2, f(x)=-(2)²+5=1
so 1<y≤4
the second piece: f(x)=2x-3
when x=2, f(x)=2(2)-3=1
when x=5, f(x)=2(5)-3=7
so 1≤y<7
union of the two parts of y: 1≤y<7
[1,7) is the answer.
Option D:
is equivalent to the given expression.
Solution:
Given expression:
To find which expression is equivalent to the given expression.
Using exponent rule: 
Using exponent rule: 
Using exponent rule: 
Divide both numerator and denominator by the common factor 5.
Therefore, is equivalent to the given expression.
Hence Option D is the correct answer.
This is basically the form of a compounded interest. Honestly the best answer i can give is: plug it into your calculator.
I'll give you a few "do it by hand" tips. Simplify 0.08/2 into 0.04. Now you do 1.04 to the 12th power in your calculator. Multiply that buy 10,000 is your answer. 16010.32 is your answer. This means that
You put $10,000 into some sort of savings account that gave 0.04 interest rate. You leave it there to be compounded each year for 12 years. And now you have 16010 dollars instead of 10k. Not bad at all if you're patient. :)
