<h3>
Answer: reflection over x axis</h3>
g(x) = -f(x) is the same as g(x) = -1*f(x)
Since y = f(x), we are really saying g(x) = -1*y. Whatever the y coordinate is on f(x), multiply it by -1. This turns something like y = 2 into y = -2, or something like y = -3 into y = 3, etc etc. Visually this reflects the point over the horizontal x axis. Do this to all points on f(x), and the entire curve reflects over the x axis.
I show an example of y = x^2 turn into y = -x^2 in the attached image below.
Answer:
Step-by-step explanation:
Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to 
and 
(doesn't matter which you assign) and use the slope formula:
Let:
The slope is equal to:
Therefore, the slope of this line is -1. In slope-intercept form 
, 
represents slope, so one of the lines must have a term with 
in it, which eliminates answer choices A and D.
For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:
Using the slope formula:
Thus, the slope of the line is 1/3 and the other line must have a term with 
in it, eliminating answer choice C and leaving the answer 
*You can find the exact equation of each line by using the slope formula as shown and plugging in any point the line passes through into
Gradient = change in y /change in x so -6-2 =-8 / -16-4 = -20 so -8/-20 = 0.4 so gradient = 0.4
