Chapter 4.1, Problem 59E

To determine

To describe:graphs of $y=2x^3\text{ and }y=2x^3+1$ are related.

Answer to Problem 59E

There is no horizontal change, but a vertical shift of 3 units

Explanation of Solution

Given information: graphs of $y=2x^3\text{ and }y=2x^3+1$

Calculation:

Polynomials can be written as:

  $f\left(x\right)=a{\left(x-h\right)}^n+v$ where

h is the horizontal move, and v is the vertical shift of the parent graph: $f\left(x\right)=a{x}^3$ .

Given $2x^3$ and $f\left(x\right)=2x^3+3,$

We can see that there is no horizontal change, but a vertical shift of 3 units.