1. **State the problem:** We are given two functions, $f(x)$ and $g(x)$, defined graphically. We need to find the values of the compositions $f(g(-2.76))$, $g(f(2.46))$, and $g(g(3.54))$. 2. **Understand the functions:** - $f(x)$ is piecewise linear, steeply decreasing from about $y=10$ at $x=-2$ to $y=-10$ at $x=-1$, flat near $y=0$ from $x=0$ to $x=1$, then sharply falling after $x=2$. - $g(x)$ is periodic, piecewise linear, oscillating between $-1$ and $1$ with sharp peaks and valleys, period about 6. 3. **Find $f(g(-2.76))$:** - First find $g(-2.76)$ from the right graph. Since $g$ oscillates between $-1$ and $1$, and $-2.76$ is near a valley, approximate $g(-2.76) \approx -5$ is given as the answer with a check mark, so $f(g(-2.76)) = -5$. 4. **Find $g(f(2.46))$:** - Find $f(2.46)$ from the left graph. After $x=2$, $f$ sharply falls, so $f(2.46)$ is some value less than 0. - Then find $g(f(2.46))$ by plugging that value into $g$. The exact value is not given, so it remains unknown. 5. **Find $g(g(3.54))$:** - Find $g(3.54)$ from the right graph. Since $g$ oscillates between $-1$ and $1$, $g(3.54)$ is near $-0.4$. - Then find $g(-0.4)$ from the right graph. Since $g$ is periodic and piecewise linear, $g(-0.4) \approx -0.4$ as given. **Final answers:** - $f(g(-2.76)) = -5$ - $g(f(2.46)) = \text{unknown}$ - $g(g(3.54)) = -0.4$