Write a rule for g.

Question

Let the graph of g be a translation 5 units up, followed by a reflection in the y-axis of the graph of f(x)=x^4-2x^3-12

Answer 1

In order to define the transformation of f(x) to g(x) we need to:

(a) shift the graph up 5 units, and

(b) reflect the graph about the y-axis

To shift the graph up or down you need only to add or subtract the number of units respectively to the function definition.

To reflect the graph about the y-axis you must replace any x in the definition with -x, so:

f(x) = x⁴ - 2x ³ -12

g(x) = (-x)⁴ -2(-x)³ – 12 + 5

g(x) = x⁴ + 2x ³ - 7

Answer 2

Hi,

to move this graph up by 5 we just add 5 to what we were given, giving us f(x) = x^4 - 2x^3 - 7. All reflect over y means is to change the direction the graph is pointing with respect to the y-axis. Right now it is pointing up, we want it to be pointing down. To reflect it over the y-axis we then negate the function. g(x) is then -x^4 + 2x^3 - 7.