Question

name annabelln powers id: 1 all rights reserved. ice date 1/16/26 period a hen graph the function and its inverse. 2) f(x) = -x - 4 find inverse

Explanation:

Step1: Replace $f(x)$ with $y$

$y = -x - 4$

Step2: Swap $x$ and $y$

$x = -y - 4$

Step3: Solve for $y$

$x + 4 = -y$
$y = -x - 4$

Step4: Identify key points for $f(x)$

For $f(x) = -x - 4$:

• When $x=0$, $y=-4$ → $(0, -4)$
• When $y=0$, $0=-x-4$ → $x=-4$ → $(-4, 0)$

Step5: Inverse points (swap coordinates)

Since the inverse is the same function, the points are identical: $(0, -4)$, $(-4, 0)$. Also, the line $y=x$ is the axis of symmetry for a function and its inverse.

Answer:

The inverse function is $f^{-1}(x) = -x - 4$.
To graph:

1. Plot the line $f(x) = -x -4$ using points $(-4, 0)$ and $(0, -4)$, then draw a straight line through them.
2. Since the inverse function is identical to $f(x)$, its graph is the same line. Additionally, the line $y=x$ (a diagonal line through the origin with slope 1) can be drawn as the symmetry axis for reference.