Question

Find g(x), where g(x) is the translation 2 units left and 13 units up of f(x)=–7x+7.

Answer 1

Answer:

$g(x)=-7x+6$

Step-by-step explanation:

Translations

For a > 0

$f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}$

$f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}$

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

Parent function:

$f(x)=-7x+7$

Translation of 2 units left:

$\implies f(x+2)=-7(x+2)+7$

Translation of 13 units up:

$\implies f(x+2)+13=-7(x+2)+7+13$

Simplifying:

$\implies g(x)=-7(x+2)+7+13$

$\implies g(x)=-7x-14+7+13$

$\implies g(x)=-7x+6$

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