Graph f(x)=int (x-2)

$f (x) = i n t$ $(x - 2)$

Find the asymptotes.

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Find the standard form of the hyperbola.

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Subtract $i n t$ from both sides of the equation.

$y - i n t = 0$

Divide each term by $0$ to make the right side equal to one.

$\frac{y}{0} - \frac{i n t}{0} = \frac{0}{0}$

Simplify each term in the equation in order to set the right side equal to $1$ . The standard form of an ellipse or hyperbola requires the right side of the equation be $1$ .

$y - i n t = 1$

This is the form of a hyperbola. Use this form to determine the values used to find the asymptotes of the hyperbola.

$\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1$

Match the values in this hyperbola to those of the standard form. The variable $h$ represents the x-offset from the origin, $k$ represents the y-offset from origin, $a$ .

$a = 1$

$b = 1$

$k = 0$

$h = 0$

The asymptotes follow the form $y = \pm \frac{b (x - h)}{a} + k$ because this hyperbola opens left and right.

$y = \pm 1 \cdot x + 0$

Simplify $1 \cdot x + 0$ .

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Add $1 \cdot x$ and $0$ .

$y = 1 \cdot x$

Multiply $x$ by $1$ .

$y = x$

Simplify $- 1 \cdot x + 0$ .

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Add $- 1 \cdot x$ and $0$ .

$y = - 1 \cdot x$

Rewrite $- 1 x$ as $- x$ .

$y = - x$

This hyperbola has two asymptotes.

$y = x, y = - x$

The asymptotes are $y = x$ and $y = - x$ .

Asymptotes: $y = x, y = - x$

Graph $x - 2$ .

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Remove parentheses.

$y = x - 2$

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

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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 $y = m x + b$ .

$m = 1$

$b = - 2$

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

Slope: $1$

y-intercept: $(0, - 2)$

Slope: $1$

y-intercept: $(0, - 2)$

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

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Find the x-intercept.

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To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = x - 2$

Solve the equation.

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Rewrite the equation as $x - 2 = 0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

Find the y-intercept.

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To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = (0) - 2$

Solve the equation.

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Remove parentheses.

$y = 0 - 2$

Remove parentheses.

$y = (0) - 2$

Subtract $2$ from $0$ .

$y = - 2$

y-intercept(s) in point form.

y-intercept(s): $(0, - 2)$

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

$\begin{array}{c} x & y \\ 0 & - 2 \\ 2 & 0 \end{array}$

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

Slope: $1$

y-intercept: $(0, - 2)$

$\begin{array}{c} x & y \\ 0 & - 2 \\ 2 & 0 \end{array}$

Slope: $1$

y-intercept: $(0, - 2)$

$\begin{array}{c} x & y \\ 0 & - 2 \\ 2 & 0 \end{array}$

Plot each graph on the same coordinate system.

$f (x) = i n t$

$x - 2$

Graph f(x)=int (x-2)

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