1. **State the problem:** We are given a graph of a function $f$ and need to find the values $f(-14)$, $f(0)$, and $f(-7)$ from the graph. 2. **Analyze the graph:** The graph is a straight line that crosses the y-axis at about $y=4$ and the x-axis at about $x=4$. This suggests the function is linear. 3. **Find the equation of the line:** The line passes through points approximately $(-14,10)$ and $(4,0)$. 4. **Calculate the slope $m$:** $$m = \frac{0 - 10}{4 - (-14)} = \frac{-10}{18} = -\frac{5}{9}$$ 5. **Use point-slope form to find $f(x)$:** Using point $(4,0)$: $$y - 0 = -\frac{5}{9}(x - 4)$$ $$f(x) = -\frac{5}{9}x + \frac{20}{9}$$ 6. **Calculate $f(-14)$:** $$f(-14) = -\frac{5}{9}(-14) + \frac{20}{9} = \frac{70}{9} + \frac{20}{9} = \frac{90}{9} = 10$$ 7. **Calculate $f(0)$:** $$f(0) = -\frac{5}{9}(0) + \frac{20}{9} = \frac{20}{9} \approx 2.22$$ 8. **Calculate $f(-7)$:** $$f(-7) = -\frac{5}{9}(-7) + \frac{20}{9} = \frac{35}{9} + \frac{20}{9} = \frac{55}{9} \approx 6.11$$ **Final answers:** - $f(-14) = 10$ - $f(0) = \frac{20}{9} \approx 2.22$ - $f(-7) = \frac{55}{9} \approx 6.11$