Graph The graph of y=f(x) is graphed below. What is the end behavior of f(x) ?

The graph of $y = f (x)$ is graphed below. What is the end behavior of $f (x)$ ?

Step 1

Graph $f (x)$ .

Divide each term in $y x = 0$ by $x$ and simplify.

Divide each term in $y x = 0$ by $x$ .

$\frac{y x}{x} = \frac{0}{x}$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{y x}{x} = \frac{0}{x}$

Divide $y$ by $1$ .

$y = \frac{0}{x}$

Simplify the right side.

Divide $0$ by $x$ .

$y = 0$

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 $y = m x + b$ .

$m = 0$

$b = 0$

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

Slope: $0$

y-intercept: $(0, 0)$

Slope: $0$

y-intercept: $(0, 0)$

Find two points on the line.

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 0 \end{array}$

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

Slope: $0$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 0 \end{array}$

Slope: $0$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 0 \end{array}$

Step 2

Plot each graph on the same coordinate system.

$y = f (x)$

$f (x)$

Step 3