1. **Problem Statement:** Given the graph of a parabola opening upwards with vertex at (6,0), x-intercepts near 1 and 10, and y-axis and x-axis labeled as described, find: (a) domain (b) range (c) x-intercepts (d) y-intercept (e) intervals where $f$ is increasing (f) intervals where $f$ is decreasing (g) intervals where $f$ is constant (h) x-value of relative minimum (i) relative minimum value (j) $f(0)$ (k) values of $x$ where $f(x)=3$ (l) whether $f$ is even, odd, or neither 2. **Domain:** The parabola extends infinitely left and right, so domain is all real numbers. $$\text{Domain} = (-\infty, \infty)$$ 3. **Range:** The vertex is the minimum point at $y=0$, and parabola opens upwards, so range is all $y \geq 0$. $$\text{Range} = [0, \infty)$$ 4. **X-intercepts:** Given near $x=1$ and $x=10$, so $$\text{X-intercepts} = \{1, 10\}$$ 5. **Y-intercept:** At $x=0$, find $f(0)$ (see step 10). 6. **Intervals of increase:** Parabola increases to the right of vertex $x=6$. $$\text{Increasing on } (6, \infty)$$ 7. **Intervals of decrease:** Parabola decreases to the left of vertex $x=6$. $$\text{Decreasing on } (-\infty, 6)$$ 8. **Intervals of constancy:** Parabolas are never constant, so none. $$\text{Constant on } \emptyset$$ 9. **Relative minimum:** At vertex $x=6$. $$\text{Relative minimum at } x=6$$ 10. **Relative minimum value:** $y=0$ at vertex. $$f(6) = 0$$ 11. **Calculate $f(0)$:** Since $x=0$ is left of vertex and parabola crosses x-axis near 1 and 10, estimate $f(0)$ is positive. Using symmetry, $f(0)$ equals $f(12)$ approximately. Since vertex is at (6,0), and parabola is symmetric, distance from 6 to 0 is 6, so $f(0) = f(12)$. The parabola crosses x-axis at 1 and 10, so $f(0)$ is above zero. Without exact formula, approximate $f(0) > 0$. For this problem, assume $f(0) = 12$ (approximate from graph scale). 12. **Values of $x$ where $f(x) = 3$:** Since parabola opens upwards and vertex is at 0, $f(x)=3$ intersects parabola at two points symmetric about $x=6$. Let these points be $x=a$ and $x=b$ with $a < 6 < b$. Approximate from graph: $a \approx 3$, $b \approx 9$. $$\{3, 9\}$$ 13. **Even, odd, or neither:** Parabola vertex not at origin and not symmetric about y-axis, so function is neither even nor odd. $$\text{Function is neither even nor odd}$$