Question

a function is defined by g(a)= -2a+7, and its domain is the set of integers from 1 through 30, inclusive. For how many values of a is g(a) negative

Answer 1

Answer: 27

Explanation:

integer: a whole number.

inclusive: includes

g(a) < 0

-2a +7 < 0

-2a < -7

a > 7/2

7/2 = 3.5. The next whole number is 4.

Therefore, after 4, and including 4, g(a) is negative. All the integers from 4 to 30, inclusive, is 27.

Answer 2

We have

`-2a+7<0 \iff -2a<-7 \iff 2a>7 \iff a>(7)/(2)=3.5`

So, for every number greater than 3.5, the function is negative.

In particular, if your domain is the set of integers from 1 to 30, all the integers from 4 to 30, inclusive, will produce a negative result.