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» 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

Respuesta :

xero099

Answer:

Avery is right, because [tex]g(x) = f(x)+2[/tex].

Cindy is right, because [tex]g(x) = f(x+1)[/tex].

Step-by-step explanation:

Let [tex]f(x)[/tex] and [tex]g(x)[/tex] functions, then [tex]g(x)[/tex] is the vertical translated version of [tex]f(x)[/tex] if and only if:

[tex]g(x) = f(x)+k[/tex], [tex]\forall \,k\in \mathbb{R}[/tex]

[tex]k = g(x)-f(x)[/tex]

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

[tex]k = (2\cdot x + 3) - (2\cdot x +1)[/tex]

[tex]k = 2[/tex]

Then, Avery is right, because [tex]g(x) = f(x)+2[/tex].

Let [tex]f(x)[/tex] and [tex]g(x)[/tex] functions, then [tex]g(x)[/tex] is the horizontal translated version of [tex]f(x)[/tex] if and only if:

[tex]g(x) = f(x+k)[/tex], [tex]\forall \,k\in \mathbb{R}[/tex]

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

[tex]g(x) = 2\cdot x + 3[/tex]

[tex]g(x) = 2\cdot x + 2 + 1[/tex]

[tex]g(x) = 2\cdot (x+1)+1[/tex]

[tex]g(x) = f(x+1)[/tex]

Then, Cindy is right, because [tex]g(x) = f(x+1)[/tex].

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