Graph g(x)=f(x-1)+3

$g (x) = f (x - 1) + 3$

Rewrite the function as an equation.

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

Simplify each term.

Apply the distributive property.

$y = f x + f \cdot - 1 + 3$

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

$y = f x - 1 \cdot f + 3$

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

$y = f x - f + 3$

The slope and y-intercept cannot be found for this problem since it is not linear.

Not Linear

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m =$

$b =$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope:

y-intercept: $(0,)$

Slope:

y-intercept: $(0,)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Create a table of the $x$ and $y$ values.

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

Graph the line using the slope and the y-intercept, or the points.

Slope:

y-intercept: $(0,)$

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