Chapter 3.2, Problem 1CFU

To determine

To find: an equation of graph for the given conditions.

Answer to Problem 1CFU

  $y={\left(x+4\right)}^3-7$

Explanation of Solution

Given information:

Parent graph equation is $y=x^3$ .

Units translated to left = 4

Units translated to down =7

Calculation:

The formula to move the function horizontally is ${\left(x-a\right)}^n$ . For movement towards right take positive value of unit and for movement towards left the value of units will be negative.

The formula to move the function vertically is $x^n\pm a$ . For upward movement add the unit and for downward movement subtract the units from $x^n$ Here a is the unit of transition and n is the power of x given in the parent equation.

The function is $y=f\left(x^3\right)$ . Since the transition is 4 units left and 7 units down, the function will be

  $\begin{array}{c}y=f\left(x^3\right)-7\left[\because 7\text{ unit move down}\right]\\ ={\left(x+4\right)}^3-7\left[\because 4\text{ unit move left}\right]\end{array}$

Thus the equation of graph obtained from parent graph for the given condition is $y={\left(x+4\right)}^3-7$ .