The problem asks us to graph the function $f(x) = -4x - 3$.

1. Problem Description

The problem asks us to graph the function $f(x) = -4x - 3$.

2. Solution Steps

The function $f(x) = -4x - 3$ is a linear function. We can find two points on the line to graph it.

When $x=0$, $f(0) = -4(0) - 3 = -3$. So the point $(0, -3)$ is on the line. This is the y-intercept.

When $x=1$, $f(1) = -4(1) - 3 = -4 - 3 = -7$. So the point $(1, -7)$ is on the line.

Now we can use the points $(0, -3)$ and $(1, -7)$ to graph the line.

Another way to think about this is to consider the slope-intercept form of a line, which is

$y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In our case, $f(x) = -4x - 3$, so $m = -4$ and $b = -3$. This means the line crosses the y-axis at $(0, -3)$ and has a slope of $-4$. A slope of $-4$ means that for every 1 unit increase in $x$, $y$ decreases by 4 units. So, starting at $(0, -3)$, if we increase $x$ by 1, we get to $x=1$, and then $y$ decreases by 4, so $y = -3 - 4 = -7$, which means the point $(1, -7)$ is on the line.

3. Final Answer

$f(x) = -4x - 3$