Write a rule for g

Question

Let the graph of g be a translation 2 units up followed by a reflection about the y-axis of the graph of f(x)=8x+3. Write a rule for g.

Answer 1

Start with the function:      f(x) = 8x + 3

 

That means:  slope, m, is 8 and y-intercept is the point (0,3).

 

"translation 2 units up" means that the function, let's call it h(x), will have a value 2 more than f(x) for each x.  This is easy:

      h(x) = 8x + 5             [h(x) is always 2 more than f(x)]

 

Now, to reflect about the y-axis:  the value of the function is the same as it previously was for the negative of x.

     g(x) = -h(x)

     g(x) = -(8x-5)

     g(x) = -8x + 5

 

Notice that the slope is now (-8), which is downward.  Folding a plot on the y-axis gives us reassurance that this is reflective about the y-axis.