Find Three Ordered Pair Solutions g(x)=f(x-1)-2

$g (x) = f (x - 1) - 2$

Step 1

Write $g (x) = f (x - 1) - 2$ as an equation.

$y = f (x - 1) - 2$

Step 2

Simplify each term.

Apply the distributive property.

$y = f x + f \cdot - 1 - 2$

Move $- 1$ to the left of $f$ .

$y = f x - 1 \cdot f - 2$

Rewrite $- 1 f$ as $- f$ .

$y = f x - f - 2$

Step 3

Choose any values for $x$ and $y$ that are in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ and $1$ to substitute for $z$ .

Remove parentheses.

$y = f (0) - f - 2$

Simplify $f (0) - f - 2$ .

Multiply $f$ by $0$ .

$y = 0 - f - 2$

Subtract $f$ from $0$ .

$y = - f - 2$

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(0, - f - 2, 1)$

Step 5

Choose $1$ to substitute in for $x$ and $2$ to substitute for $z$ .

Remove parentheses.

$y = f (1) - f - 2$

Simplify $f (1) - f - 2$ .

Multiply $f$ by $1$ .

$y = f - f - 2$

Subtract $f$ from $f$ .

$y = 0 - 2$

Subtract $2$ from $0$ .

$y = - 2$

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(1, - 2, 2)$

Step 6

Choose $2$ to substitute in for $x$ and $3$ to substitute for $z$ .

Remove parentheses.

$y = f (2) - f - 2$

Simplify $f (2) - f - 2$ .

Move $2$ to the left of $f$ .

$y = 2 f - f - 2$

Subtract $f$ from $2 f$ .

$y = f - 2$

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(2, f - 2, 3)$

Step 7

These are three possible solutions to the equation.

$(0, - f - 2, 1), (1, - 2, 2), (2, f - 2, 3)$

Find Three Ordered Pair Solutions g(x)=f(x-1)-2

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