MATH SOLVE

3 months ago

Q:
# 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^3transformation: shift the graph 5 units to the left and upward 4 units

Accepted Solution

A:

ANSWER[tex]g(x) = {(x + 5)}^{3} + 4[/tex]EXPLANATIONGiven the parent function:[tex]f(x) = {x}^{3} [/tex]If we shift the graph of f(x), 5 units to the left, then the new rule is [tex]x \to \: {(x + 5)}^{3} [/tex]If we again, shift this graph upward by 4 units, then the completely transformed function will have the rule,[tex]x \to \: {(x + 5)}^{3} + 4[/tex]Or[tex]g(x) = {(x + 5)}^{3} + 4[/tex]