1. **Problem:** Identify the graph type for each polynomial function given. 2. **Step 1:** Understand the shape of polynomial graphs based on degree and leading coefficient. - Odd degree polynomials have end behaviors opposite on each side. - Even degree polynomials have the same end behavior on both sides. - Positive leading coefficient means the graph rises to the right; negative means it falls. - Number of peaks and valleys is at most degree minus one. 3. **Step 2:** Analyze each function: - $f(x) = -2x + 3$: Linear, negative slope, straight line descending left to right (c). - $f(x) = x^2 - 4x$: Quadratic, positive leading coefficient, parabola opening upwards (d). - $f(x) = -2x^2 - \sqrt{5}x$: Quadratic, negative leading coefficient, parabola opening downwards (h). - $f(x) = 2x^3 - 3x + 4$: Cubic, positive leading coefficient, one peak and one valley (b). - $f(x) = -4x^4 + 3x^2$: Quartic, negative leading coefficient, descending then sharply going down (e). - $f(x) = -8x^7 + x^2 - 4$: Degree 7, negative leading coefficient, peak and valley, opening upwards (f). - $f(x) = x^4 + 2x^3$: Quartic, positive leading coefficient, two peaks and one valley (a). - $f(x) = -5x^6 - 2x^3 + 7x$: Degree 6, negative leading coefficient, parabola opening downwards (h). 4. **Step 3:** Match graphs: - (a) Two peaks and one valley: $f(x) = x^4 + 2x^3$ - (b) One peak and one valley: $f(x) = 2x^3 - 3x + 4$ - (c) Straight line descending: $f(x) = -2x + 3$ - (d) Parabola opening upwards: $f(x) = x^2 - 4x$ - (e) Descending then sharply down: $f(x) = -4x^4 + 3x^2$ - (f) Peak and valley, opening upwards: $f(x) = -8x^7 + x^2 - 4$ - (g) Parabola opening upwards: (No exact match given, possibly $f(x) = x^2 - 4x$ again) - (h) Parabola opening downwards: $f(x) = -2x^2 - \sqrt{5}x$ and $f(x) = -5x^6 - 2x^3 + 7x$ --- 5. **Problem:** Fill in the blanks for parts of a circle. 6. **Step 1:** Definitions and answers: 1. Circle: Set of all **points** that are the same **distance** from the **center** point. 2. Center of the Circle: The **center** point. 3. Radius: Line segment from the **center** to a point on the **circle**. 4. Chord: Line segment whose **endpoints** are on the circle. 5. Diameter: A **chord** that passes through the **center** of the circle. 6. Secant Line: A **line** that intersects the circle. 7. Tangent Line/Point of Tangency: A **line** that touches the circle **at one point** / Point where the tangent line touches. 8. Arc: Piece of the **circumference** (outside) of the circle (minor, major, semicircle). 9. Sector: Piece of the **area** of the circle. --- **Final answers:** - Graph matches: (a) $x^4 + 2x^3$, (b) $2x^3 - 3x + 4$, (c) $-2x + 3$, (d) $x^2 - 4x$, (e) $-4x^4 + 3x^2$, (f) $-8x^7 + x^2 - 4$, (h) $-2x^2 - \sqrt{5}x$ and $-5x^6 - 2x^3 + 7x$. - Circle blanks: points, distance, center, center, circle, endpoints, chord, center, line, at one point, line, circumference, area.