Graph Using a Table of Values y=f(x+3)

$y = f (x + 3)$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = f ((- 2) + 3)$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$y = f (- 2 + 3)$

Remove parentheses.

$y = f ((- 2) + 3)$

Simplify $f ((- 2) + 3)$ .

Add $- 2$ and $3$ .

$y = f \cdot 1$

Multiply $f$ by $1$ .

$y = f$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = f ((- 1) + 3)$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$y = f (- 1 + 3)$

Remove parentheses.

$y = f ((- 1) + 3)$

Simplify $f ((- 1) + 3)$ .

Add $- 1$ and $3$ .

$y = f \cdot 2$

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

$y = 2 f$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = f ((0) + 3)$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = f (0 + 3)$

Remove parentheses.

$y = f ((0) + 3)$

Simplify $f ((0) + 3)$ .

Add $0$ and $3$ .

$y = f \cdot 3$

Move $3$ to the left of $f$ .

$y = 3 f$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = f ((1) + 3)$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = f (1 + 3)$

Remove parentheses.

$y = f ((1) + 3)$

Simplify $f ((1) + 3)$ .

Add $1$ and $3$ .

$y = f \cdot 4$

Move $4$ to the left of $f$ .

$y = 4 f$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = f ((2) + 3)$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = f (2 + 3)$

Remove parentheses.

$y = f ((2) + 3)$

Simplify $f ((2) + 3)$ .

Add $2$ and $3$ .

$y = f \cdot 5$

Move $5$ to the left of $f$ .

$y = 5 f$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & f \\ - 1 & 2 f \\ 0 & 3 f \\ 1 & 4 f \\ 2 & 5 f \end{array}$

Step 12

Graph Using a Table of Values y=f(x+3)

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