1. The problem asks which values of $n$ can be used in $f(x) = x^n$ if $f$ is a polynomial function. 2. A polynomial function requires $n$ to be a whole number (non-negative integer). 3. Checking options: - A. $-2$ is negative, not allowed. - B. $0$ is allowed (constant function). - C. $\frac{1}{4}$ is a fraction, not allowed. - D. $\sqrt{3}$ is irrational, not allowed. 4. So, only $n=0$ is valid. 5. For $y = x^3 - 7x + 6$, the leading term is the term with the highest power of $x$. 6. The highest power is $3$, so leading term is $x^3$. 7. The y-intercept is the value of $y$ when $x=0$. 8. Substitute $x=0$: $y = 0 - 0 + 6 = 6$. 9. Which is NOT a polynomial function? - A. $f(x) = 2$ is polynomial. - B. $f(x) = \frac{1}{x^2}$ is not polynomial (negative exponent). - C. $f(x) = x^2 - x$ is polynomial. - D. $2x^3 + x^2$ is polynomial. 10. Sum of central angles of a circle is always $360$ degrees. 11. An inscribed angle intercepting a semicircle measures exactly $90$ degrees. 12. An angle formed by two rays with vertex at the center of the circle is a central angle. 13. Opposite angles of a quadrilateral inscribed in a circle are supplementary (sum to $180$ degrees). 14. In circle A, $\angle TAH$ is an inscribed angle. 15. The congruent arc of $MS$ is $SH$ (arcs opposite equal chords). 16. A tangent line intersects a circle at exactly one point. 17. The point of intersection of a tangent and a circle is called the point of tangency. 18. A segment of a circle is the region bounded by an arc and the chord joining its endpoints; in the figure, $ES$ is the segment. 19. In $\odot U$, $m\angle PRE = \frac{1}{2} m\angle PUE = \frac{1}{2} \times 56 = 28$ degrees. 20. Radius is half the diameter, so radius = $\frac{12}{2} = 6$ inches. 21. Length of crust (arc length) for each slice is $\frac{1}{8}$ of circumference. 22. Circumference $= 2\pi r = 2\pi \times 6 = 12\pi$. 23. Length of crust per slice $= \frac{12\pi}{8} = \frac{3}{2}\pi$. 24. Distance formula between points $A(2,5)$ and $B(-4,9)$ is $d = \sqrt{(-4 - 2)^2 + (9 - 5)^2}$. 25. Proof using figures on coordinate plane is coordinate proof. 26. Standard equation of circle with center $(h,k)$ and radius $r$ is $(x - h)^2 + (y - k)^2 = r^2$. 27. Circle with center at origin and radius 6 has equation $x^2 + y^2 = 36$. 28. Distance from center for $(x-3)^2 + (y+5)^2 = 25$ is radius $= 5$. 29. Equation of circle with center $(-6,-8)$ and radius 8 is $(x + 6)^2 + (y + 8)^2 = 64$. 30. Point B lies in Quadrant II. 31. The quadrilateral formed is a parallelogram. 32. Arc length formula: $L = \frac{\theta}{360} \times 2\pi r$. 33. For arc $45^\circ$ and radius 8 cm, $L = \frac{45}{360} \times 2\pi \times 8 = 2\pi$ cm. 34. Each central angle in a regular octagon is $\frac{360}{8} = 45$ degrees. 35. Midpoint between $(-12,15)$ and $(18,3)$ is $\left(\frac{-12+18}{2}, \frac{15+3}{2}\right) = (3,9)$. 36. Distance between $S(1,5)$ and $R(1,-2)$ is $|5 - (-2)| = 7$. 37. Distance between $R(-3,2)$ and $S(4,1)$ is $\sqrt{(4+3)^2 + (1-2)^2} = \sqrt{49 + 1} = \sqrt{50} = 5\sqrt{2}$. 38. Coordinates of point Y in hexagon is $Y(m,-r)$. 39. Missing coordinate to form right triangle is $(2,0)$. 40. Angle $\angle RLQ$ is $70$ degrees. 41. Degree for food in pie graph: $\frac{10000}{45000} \times 360 = 80$ degrees. 42. General equation of circle with center $(-2,-3)$ and radius 4 is $x^2 + y^2 + 4x + 6y - 29 = 0$. 43. Length of segment joining $P(10,1)$ and $T(7,-2)$ is $\sqrt{(7-10)^2 + (-2-1)^2} = \sqrt{9 + 9} = \sqrt{18} = 4.24$. Final answers: 1. B 2. A 3. D 4. B 5. D 6. B 7. A 8. A 9. C 10. B 11. B 12. C 13. C 14. A 15. D 16. D 17. B 18. C 19. B 20. C 21. C 22. A 23. B 24. A 35. A 36. D 37. C 38. C 39. A 40. D