Not an actual test question but just curious:
1 answer:
well, when we use the word "the function" we're referring to the dependent part, which depends on the independent, y,x wise, we're referring to the function "y" or f(x) if you wish.
so for an exponential function
is the function ever positive only? it can be
is it negative only? it can be
can it be both? sure thing, most of the time it's both
we can say a function f(x) is always positive when the independent values of "x" yield a positive value only, mind you that when we're talking about "the function" we're really referring to the resulting values in a set, so can the values of the output no matter what "x" we use be always positive? sure, can they also be negative only? sure, how about both? sure thing.
notice the template in the picture below, we can transform any exponential function like the one above 2ˣ with some vertical shift upwards, and is always positive, or -2ˣ with a vertical shift downwards and it's always negative, or we can stretch it about and have -2ˣ shifted upwards so sometimes is positive, and sometimes is negative.
above the x-axis is always positive, below is negative, but with transformations on the parent function it can be any of the three types.
You might be interested in
Given:
The system of equations is
To find:
The true statement about the given system of equations.
Solution:
The slope intercept form of a line is
Where, m is the slope and b is the y-intercept.
We have,
On comparing these two lines with slope intercept form, we get
Since the slopes of the lines are equal but the y-intercepts are different, therefore, the two lines are parallel and the system has no solution.
Therefore, the correct option is A.