Question

identify the intercepts of $f(x)$, which is graphed below.
$f(x) = -|x + 1| - 4$

1. enter each $x$-intercept as an ordered pair in its own input box. if there are no $x$-intercepts, enter the $\\o$ symbol.

$x$-intercept:

1. enter the $y$-intercept as an ordered pair.

Explanation:

Step1: Find x - intercepts

To find the x - intercepts, we set \(y = f(x)=0\) and solve for \(x\). So we have the equation:

$$0=-\vert x + 1\vert-4$$

Add \(\vert x + 1\vert\) to both sides:

$$\vert x+1\vert=- 4$$

But the absolute value of a number is always non - negative (i.e., \(\vert a\vert\geq0\) for any real number \(a\)). Since \(-4<0\), there is no real solution for \(x\) when \(y = 0\). So the x - intercepts are \(\varnothing\) (the empty set).

Step2: Find y - intercept

To find the y - intercept, we set \(x = 0\) in the function \(f(x)=-\vert x + 1\vert-4\).
Substitute \(x = 0\) into the function:

$$f(0)=-\vert0 + 1\vert-4=-\vert1\vert-4=-1 - 4=-5$$

So the y - intercept is the ordered pair \((0,-5)\).

Answer:

1. \(x\) - intercept: \(\varnothing\)
2. \(y\) - intercept: \((0, - 5)\)