1. **Problem statement:** Identify the degree, leading coefficient, and end behavior of each polynomial function. 2. **Key concepts:** - The **degree** of a polynomial is the highest power of $x$. - The **leading coefficient** is the coefficient of the term with the highest degree. - The **end behavior** depends on the degree and leading coefficient: - If degree is even and leading coefficient is positive, both ends go to $+\infty$. - If degree is even and leading coefficient is negative, both ends go to $-\infty$. - If degree is odd and leading coefficient is positive, left end goes to $-\infty$, right end to $+\infty$. - If degree is odd and leading coefficient is negative, left end goes to $+\infty$, right end to $-\infty$. 3. **Part a:** $f(x) = -4x^3 + 3x^2 - 15x + 5$ - Degree: highest power is 3. - Leading coefficient: coefficient of $x^3$ is $-4$. - End behavior: degree odd, leading coefficient negative. - As $x \to -\infty$, $f(x) \to +\infty$. - As $x \to +\infty$, $f(x) \to -\infty$. 4. **Part b:** $g(x) = 2x^5 - 4x^3 + 10x^2 - 13x + 8$ - Degree: highest power is 5. - Leading coefficient: coefficient of $x^5$ is $2$. - End behavior: degree odd, leading coefficient positive. - As $x \to -\infty$, $g(x) \to -\infty$. - As $x \to +\infty$, $g(x) \to +\infty$. 5. **Part c:** $p(x) = 4 - 5x + 4x^2 - 3x^3$ - Degree: highest power is 3. - Leading coefficient: coefficient of $x^3$ is $-3$. - End behavior: degree odd, leading coefficient negative. - As $x \to -\infty$, $p(x) \to +\infty$. - As $x \to +\infty$, $p(x) \to -\infty$. 6. **Part d:** $b(x) = (2x - 5)(3x + 2)(4x - 3)$ - First find degree and leading coefficient by multiplying leading terms: - Leading terms: $2x$, $3x$, $4x$. - Degree: $1 + 1 + 1 = 3$. - Leading coefficient: $2 \times 3 \times 4 = 24$. - End behavior: degree odd, leading coefficient positive. - As $x \to -\infty$, $b(x) \to -\infty$. - As $x \to +\infty$, $b(x) \to +\infty$. **Final answers:** - a) Degree = 3, Leading coefficient = $-4$, End behavior: left $+\infty$, right $-\infty$. - b) Degree = 5, Leading coefficient = 2, End behavior: left $-\infty$, right $+\infty$. - c) Degree = 3, Leading coefficient = $-3$, End behavior: left $+\infty$, right $-\infty$. - d) Degree = 3, Leading coefficient = 24, End behavior: left $-\infty$, right $+\infty$.