1. **State the problem:** We are given the linear function $f(x) = -2x + 5$ and asked to analyze its intercepts and end behavior. 2. **Find the x-intercept:** The x-intercept occurs where $f(x) = 0$. $$0 = -2x + 5$$ Add $2x$ to both sides: $$2x = 5$$ Divide both sides by 2: $$x = \frac{\cancel{2}x}{\cancel{2}} = \frac{5}{2} = 2.5$$ So the x-intercept is at $(2.5, 0)$. 3. **Find the y-intercept:** The y-intercept occurs where $x = 0$. $$f(0) = -2(0) + 5 = 5$$ So the y-intercept is at $(0, 5)$. 4. **Analyze end behavior:** Since the function is linear with slope $-2$ (negative), as $x \to -\infty$, the value of $f(x)$ increases without bound: $$\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} (-2x + 5) = \infty$$ As $x \to \infty$, the value of $f(x)$ decreases without bound: $$\lim_{x \to \infty} f(x) = \lim_{x \to \infty} (-2x + 5) = -\infty$$ 5. **Summary:** - x-intercept: $(2.5, 0)$ - y-intercept: $(0, 5)$ - End behavior: as $x \to -\infty$, $y \to \infty$; as $x \to \infty$, $y \to -\infty$. This matches the behavior of a line with negative slope crossing the y-axis at 5 and x-axis at 2.5.