00:01
In this problem, we're given the function h of x equals minus 10 minus x.
00:07
The first part of this problem is to identify whether or not h of x is a one -to -one function.
00:12
The easiest way to do that is to graph each of x on a corner of plane and use the horizontal line test.
00:19
So my graphing calculator, i'm going to say that y equals minus 10 minus x and graph that function.
00:32
Now i can see that h of x is simply a linear function with slope minus 1 and y intercept minus 10.
00:41
So to use the horizontal line test, we need to imagine drawing horizontal lines anywhere through the graph.
00:48
And we can see that if i was to draw any horizontal line, whether that be the x -axis itself, or y equals 50, or y equals 100, or y equals negative 100, any horizontal line only intersects the graph the function once.
01:04
That tells us that for any unique x value, it has a unique corresponding y value.
01:13
So that means that h of x actually does indeed, it passes the hlt, which means that h of x is indeed a one -to -one function...