Question

Write a rule for the function whose graph can be obtained from the given parent function by performing the given transformations. parent function: f(x)=x^3
transformation: shift the graph 5 units to the left and upward 4 units

Answer 1

ANSWER

$g(x) = {(x + 5)}^{3} + 4$

EXPLANATION

Given the parent function:

$f(x) = {x}^{3}$

If we shift the graph of f(x), 5 units to the left, then the new rule is

$x \to \: {(x + 5)}^{3}$

If we again, shift this graph upward by 4 units, then the completely transformed function will have the rule,

$x \to \: {(x + 5)}^{3} + 4$

Or

$g(x) = {(x + 5)}^{3} + 4$