Question

» Avery states that the graph of g is the same as the graph of f with every

point shifted vertically. Cindy states that the graph of g is the same as the
graph of f with every point shifted horizontally.
f(x)=2x+1
g(x)=2x+3
Give an argument to support Avery’s answer
Give an argument to support Cindy’s statement

Answer 1

Avery is right, because
`g(x) = f(x)+2`.

Cindy is right, because
`g(x) = f(x+1)`.

Explanation:

Let
`f(x)` and
`g(x)` functions, then
`g(x)` is the vertical translated version of
`f(x)` if and only if:

`g(x) = f(x)+k`,
`\forall \,k\in \mathbb{R}`

`k = g(x)-f(x)`

If we know that
`f(x) = 2\cdot x + 1` and
`g(x) = 2\cdot x + 3`, then:

`k = (2\cdot x + 3) - (2\cdot x +1)`

`k = 2`

Then, Avery is right, because
`g(x) = f(x)+2`.

Let
`f(x)` and
`g(x)` functions, then
`g(x)` is the horizontal translated version of
`f(x)` if and only if:

`g(x) = f(x+k)`,
`\forall \,k\in \mathbb{R}`

If we know that
`f(x) = 2\cdot x + 1` and
`g(x) = 2\cdot x + 3`, then:

`g(x) = 2\cdot x + 3`

`g(x) = 2\cdot x + 2 + 1`

`g(x) = 2\cdot (x+1)+1`

`g(x) = f(x+1)`

Then, Cindy is right, because
`g(x) = f(x+1)`.