Here are the solutions to the problems: 46. Which of the following represents the graph of a function? A graph represents a function if it passes the vertical line test, meaning any vertical line intersects the graph at most once. Graph (A) fails the vertical line test. Graph (B) fails the vertical line test. Graph (C) passes the vertical line test. Graph (D) fails the vertical line test. The correct option is (C). $$\boxed{\text{C)}}$$ 47. The straight line AB cuts the Y axis at From the graph provided for Item 47, the line intersects the Y-axis at the point where $x=0$. Observing the graph, this point is $(0, -1)$. The correct option is (D). $$\boxed{\text{D) } (0, -1)}$$ 48. The gradient of AB in the graph above is From the graph provided for Item 48, we can identify two points on the line AB. Point A appears to be $(2, 1)$. Point B appears to be $(6, 3)$. The formula for the gradient $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ Substitute the coordinates of A and B: $$ m = \frac{3 - 1}{6 - 2} $$ $$ m = \frac{2}{4} $$ $$ m = \frac{1}{2} $$ The correct option is (B). $$\boxed{\text{B) } \frac{1}{2}}$$ 49. The inequality above is defined by The diagram shows a number line with a shaded region. There is an open circle at $-2$, indicating that $-2$ is not included in the solution set. There is a closed circle at $3$, indicating that $3$ is included in the solution set. The shaded region is between $-2$ and $3$. Therefore, the inequality is $-2 < x \le 3$. The correct option is (B). $$\boxed{\text{B) } -2 < x \le 3}$$ 50. If $P = 2x^2 + 2x - 1$, then $P(1) = $ To find $P(1)$, substitute $x=1$ into the expression for $P$. $$ P(1) = 2(1)^2 + 2(1) - 1 $$ $$ P(1) = 2(1) + 2 - 1 $$ $$ P(1) = 2 + 2 - 1 $$ $$ P(1) = 4 - 1 $$ $$ P(1) = 3 $$ The correct option is (D). $$\boxed{\text{D) } 3}$$ 51. What is the gradient of the line $2y - 8x = 7$? To find the gradient, rearrange the equation into the slope-intercept form $y = mx + c$, where $m$ is the gradient. $$ 2y - 8x = 7 $$ Add $8x$ to both sides of the equation: $$ 2y = 8x + 7 $$ Divide both sides by 2: $$ y = \frac{8x}{2} + \frac{7}{2} $$ $$ y = 4x + \frac{7}{2} $$ The gradient $m$ is the coefficient of $x$. $$ m = 4 $$ The correct option is (D). $$\boxed{\text{D) } 4}$$ 3 done, 2 left today. You're making progress.