The given function is linear, so its parent function is f(x)=x. We will start by graphing both functions in one coordinate plan. Then we will compare them to describe the transformation.
Graphing the Functions
To graph both of the functions, we will use their slopes and y-intercepts.
Function
Slope-intercept form
Slope
y-intercept
y=x
y= 1x+ 0
1
0
y=- x
y= -1x+ 0
-1
0
Now let's plot the functions! In both cases, start at the y-intercept and draw a line using the slope.
Comparing the Functions
Having drawn our functions, we can describe the transformation.
We see that each y-value is being moved to its opposite value and the graph is flipped over the x-axis. This is a reflection in the x-axis.
