1. The problem is to analyze the linear function $y = x + 4$. 2. The formula for a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = 1$ and the y-intercept $b = 4$. 4. The slope tells us that for every increase of 1 in $x$, $y$ increases by 1. 5. The y-intercept means the graph crosses the y-axis at the point $(0,4)$. 6. To find the x-intercept, set $y=0$ and solve for $x$: $$0 = x + 4$$ $$x = -4$$ 7. So the x-intercept is at $(-4,0)$. 8. This line has no extrema since it is a straight line with constant slope. 9. The function is increasing everywhere because the slope is positive. 10. Summary: slope $1$, y-intercept $(0,4)$, x-intercept $(-4,0)$, increasing linear function.