Question

Suppose that f(x)=x^3 and g(x)=-2^3-7 which statement best compares the graph of g(x) with the graph of f(x)

Answer 1

Answer:

A. The graph of $G(x)$ is the graph of $F(x)$ stretched vertically, flipped over the x axis, and shifted 7 units down.

Step-by-step explanation:

Given:

$F(x)=x^3\\G(x)=-2x^3-7$

In order to transform $F(x)$ to $G(x)$, we need to follow the following transformation rules:

1. Multiply the function by the number 2. According to transformation rules, multiplying a function by a positive number greater than 1 results in vertical stretch of the function's graph.

2. Multiply by -1. Multiplying a function by -1 flips it over the x axis.

3. Add -7 to the function obtained in step 2. When a negative number C is added to a function, then the graph shift down by C units. So, here the graph shifts down by 7 units.

Thus, the graph of $G(x)$ is the graph of $F(x)$ stretched vertically, flipped over the x axis, and shifted 7 units down.