1. **State the problem:** Analyze the function $$y = -5^3 + 3^2 - 4x + 18$$ for its degree, intercepts, end behavior, and transformations. 2. **Simplify the expression:** Calculate the constants first. $$-5^3 = -(5^3) = -125$$ $$3^2 = 9$$ So the function becomes: $$y = -125 + 9 - 4x + 18$$ 3. **Combine like terms:** $$-125 + 9 + 18 = -125 + 27 = -98$$ Thus, $$y = -4x - 98$$ 4. **Degree:** The function is linear because the highest power of $x$ is 1. 5. **Intercepts:** - **y-intercept:** Set $x=0$: $$y = -4(0) - 98 = -98$$ So the y-intercept is $(0, -98)$. - **x-intercept:** Set $y=0$: $$0 = -4x - 98$$ Add 98 to both sides: $$98 = -4x$$ Divide both sides by $-4$: $$x = \frac{\cancel{98}}{\cancel{-4}} = -\frac{98}{4} = -24.5$$ So the x-intercept is $(-24.5, 0)$. 6. **End behavior:** Since the function is linear with a negative slope (-4), as $x \to \infty$, $y \to -\infty$, and as $x \to -\infty$, $y \to \infty$. 7. **Transformations:** The function is a line with slope $-4$ and y-intercept $-98$. It is a vertical shift down by 98 units and a reflection over the x-axis compared to $y=4x$ (because of the negative slope). **Final answer:** - Degree: 1 (linear) - y-intercept: $(0, -98)$ - x-intercept: $(-24.5, 0)$ - End behavior: $y \to -\infty$ as $x \to \infty$, $y \to \infty$ as $x \to -\infty$ - Transformation: linear function with slope $-4$ and vertical shift down 98 units.