Question is in description! Urgent!

Question

We need to think of a function, I have thought of x^3 + x^2+3x+2 and we need to see how y=f(4-x) affects the graph we thought of. When I put the equations in a graphing software, it comes up with a math error. Could I please have help with what the question is asking? And the answer?

Answer 1

f(4 - x) = f(-x + 4)

Starting with f(x), replace x with -x (this reflects the graph in the y-axis)

Next, replace -x by -x + 4 (this translates the graph 4 units to the left)

So, reflect y = f(x) in the y-axis and then translate the reflected graph 4 units to the left.

Answer 2

Take your starting function, and replace x with 4-x:

This gives:

y = f(4-x) = (4-x)³ + (4-x)² + 3(4-x) + 2

When you expand this, you will now have a 4th-order polynomial. (Try entering it in the graphing SW in the format I have given)

It might be better to pick a simpler starting equation......