Question

Nora was given the graph of a function. She has identified that the given graph is a cubic function. Her transformed function has been vertically stretched by a factor of 2 and vertically shifted up 3 units compared to the parent function f(x)=x^3
. Create a table to model the transformed function given in Nora’s graph. (1 point)

Answer 1

To create the table for the transformed function based on Nora's description, we first need to establish the formula for the transformed function.

Starting with the parent function:
\[ f(x) = x^3 \]

Given that the function is vertically stretched by a factor of 2 and shifted up 3 units, the transformed function \( g(x) \) can be expressed as:
\[ g(x) = 2f(x) + 3 = 2(x^3) + 3 \]
Thus:
\[ g(x) = 2x^3 + 3 \]

Now we can create a table of values for the function \( g(x) \). We'll choose a few values for \( x \) to evaluate \( g(x) \).

| \( x \) | \( g(x) = 2x^3 + 3 \) |
|---------|-------------------------|
| -2 | \( 2(-2)^3 + 3 = 2(-8) + 3 = -16 + 3 = -13 \) |
| -1 | \( 2(-1)^3 + 3 = 2(-1) + 3 = -2 + 3 = 1 \) |
| 0 | \( 2(0)^3 + 3 = 2(0) + 3 = 0 + 3 = 3 \) |
| 1 | \( 2(1)^3 + 3 = 2(1) + 3 = 2 + 3 = 5 \) |
| 2 | \( 2(2)^3 + 3 = 2(8) + 3 = 16 + 3 = 19 \) |

So, the complete table is:

| \( x \) | \( g(x) = 2x^3 + 3 \) |
|---------|-------------------------|
| -2 | -13 |
| -1 | 1 |
| 0 | 3 |
| 1 | 5 |
| 2 | 19 |

This table reflects the values of the transformed cubic function \( g(x) = 2x^3 + 3 \).