Question

In a function, how will the y-values be different if x is negative or positive?
A.
The y-values will decrease if x is negative and increase if x is positive.
B.
The y-values will increase if x is negative and decrease if x is positive.
C.
There will be no difference. If x increases, y-values will increase.
D.
You can't tell without knowing the function rule.

Answer 1

I think it is D. am I right

Answer 2

Consider two functions:
\[y = x + 1\]
\[y = -x - 1\]
Ask these questions for each function and see which one holds with both.

Answer 3

Put more simply, if you increase x in both functions, will y respond the same way in both functions?

Answer 4

yes

Answer 5

For the first function, let x = -2:
\[y = -2 + 1 = -1\]
Then let x = 2:
\[y = 2 + 1 = 3\]
So, if x is positive, y is usually positive, and if x is negative, y is negative. Increasing x leads to an increase in y.

How about for the second function?
Let x = -2:
\[y = -(-2) - 1 = 2 - 1 = 1\]
And then let x = 2:
\[y = -2 - 1 = -3\]
Here, it is the opposite! If x is positive, y is negative, and if x is negative, y is positive. Furthermore, increasing x decreases y.

Therefore, what can we say about these two functions? Which of the answers holds?

Answer 6

a

Answer 7

For the first function A & C apply. For the second function only B applies. What's the only answer that's consistent with this result?

Answer 8

it would be D