Hello!
This question is an example of composition of functions. It is using range values of some given function as domain values of some other given function to find new range values. Remember that the domain of the composite function will be the same as the domain of the first function.
Given f(g(x)), for f = , substitute x with g(x) =
.
Therefore, .
Answer:
The slope is undefined.
Step-by-step explanation:
The slope of a line is its relationship between its change in verticalness and its change in horizontalness. In layman's terms, we call it rise over run. Slope can be useful for many things: to show how steep a line is, to write a line in slope-intercept form (y = mx + b), etc.
Recall that a line only needs two points to be formed. That's why slope matters so much. With lines, we only care about its steepness and its position on the coordinate plane, so slope knocks out one of those criteria.
One way to find slope is to use the definition of slope, the change in verticalness (y) divided by the change in horizontalness (x):
where m is the slope of the line;
and x1, y1, x2, and y2 are coordinates for points (x1, y1) and (x2, y2).
So let's use what we now know to solve the problem.
Since (-5,8) and (-5,9) are two points, they can form a line. So I can say that x1 = -5, y1 = 8, x2 = 5, and y2 = 9. Now, let's plug these numbers into the formula.
"Wait, what's going on? I thought I can't divide by 0." - You
Yes, exactly. But what we have here is a special case of a line, nothing more. Let me explain.
Lines don't always have a natural number for a slope, like m = 1. There are two special lines that deviate from the norm: horizontal lines and vertical lines.
Horizontal lines have a slope of zero. This is because they change in x, but not in y. So y appears as 0 in the formula: 0/x = 0. That's why horizontal lines have a slope of zero. They are usually written as y = C where C is some constant.
Vertical lines have an undefined slope. We're dealing with this type of line for our problem. They change in y, but not in x. So x appears as 0 in the formula: y/0 = undefined. We simply cannot divide by zero. That's why vertical lines have undefined slopes. They are usually written as x = C where C is some constant.
So there you go. (-5, 8) and (-5, -9) form a vertical line that has an undefined slope. And if you really want to know the equation for this line, it's x = -5.