Question

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

Answer 1

Answer:

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

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

Step-by-step 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 $g(x) = f(x+1)$.