Write a rule for g.

Question

Let the graph of g​ be a horizontal stretch by a factor of 4, followed by a translation 3 units right and 5 units down of the graph of f(x)=x^5+3x

Answer 1

Assuming f(x) - x⁵ - 3x is the correct problem then to make it have a horizontal stretch factor of 4 means we multiply each "x" by 1/4 or 0.25:

y = (0.25x)⁵ - 3(0.25x)

To translate 3 units right means we subtract 3 from each x which means we would have:

y = (0.25(x - 3))⁵ - 3(0.25(x - 3))

To translate 5 units down means it becomes:

g(x) = (0.25(x - 3))⁵ - 3(0.25(x - 3)) - 5

If you want, you can multiply it out and combine like terms to put it in standard form.