Question

Which statement explains the difference between the graphs of f(x) = 4

and g(x) = -8

?

Responses

A The graph of g(x) is obtained by flipping f(x) over the y-axis and stretching vertically by a factor of 2.The graph of g(x) is obtained by flipping f(x) over the y-axis and stretching vertically by a factor of 2.

B The graph of g(x) is obtained by flipping f(x) over the x-axis and compressing vertically by a factor of 2.The graph of g(x) is obtained by flipping f(x) over the x-axis and compressing vertically by a factor of 2.

C The graph of g(x) is obtained by flipping f(x) over the x-axis and stretching vertically by a factor of 2.The graph of g(x) is obtained by flipping f(x) over the x-axis and stretching vertically by a factor of 2.

D The graph of f(x) is obtained by flipping g(x) over the y-axis and compressing vertically by a factor of 2.

Answer 1

The correct statement explaining the difference between the graphs of
`(f(x) = 4\)` and
`\(g(x) = -8\)` is The graph of
`\(g(x)\)` is obtained by flipping
`\(f(x)\)`over the x-axis and stretching vertically by a factor of 2 correct option is c.

Given functions:

`\(f(x) = 4\) and \(g(x) = -8\)`

let's analyze what these functions represent.

`\(f(x) = 4\)` is a horizontal line at
`\(y = 4\)` because it does not depend on
`\(x\)`. This means that no matter what
`\(x\)` value you plug into the function, the output will always be
`\(4\)` .

`\(g(x) = -8\)` is also a horizontal line, but at
`\(y = -8\)`. Similar to
`\(f(x)\)`, it doesn't depend on
`\(x\)` and always gives an output of
`\(-8\)` for any
`\(x\)` value.

the difference between these functions:

`\(f(x)\)` is a horizontal line at
`\(y = 4\).`

`\(g(x)\)` is a horizontal line at
`\(y = -8\).`

The difference in their
`\(y\)`- values is
`\(4 - (-8) = 12\)`. So, the vertical distance between these two horizontal lines is
`\(12\)`.

The only transformation happening here is a vertical shift by
`\(12\)` units because the lines are parallel and merely shifted vertically.

Therefore, neither of the original options accurately describes the relationship between
`\(f(x)\)` and
`\(g(x)\)`. The correct difference is a vertical shift of
`\(12\)` units between the two horizontal lines.