Question

Write a rule for $g$ that represents the indicated transformations of the graph of $f$ .

$f\left(x\right)=2x^5-x^3+x^2+4$ ; reflection in the y-axis and a vertical stretch by a factor of 3, followed by a translation 1 unit down

$g\left(x\right)=$

Answer 1

g(x) = 3 f(-x) - 1

Since f(-x) = -2x^5 + x^3 + x^2 + 4,
g(x) = 3(-2x^5 + x^3 + x^2 + 4) - 1 = -6x^5 + 3x^3 + 3x^2 + 11.