4.1.1 Write down the values of p and q - NSC Mathematics - Question 4 - 2022 - Paper 1

To find the x-intercept, set h(x) = 0:

$1 + p + q = 0$ Substituting the values gives: $1 - 1 + 2 = 0$ Thus, the x-intercept occurs at (0, 0).

The x-intercept of g is derived from the x-intercept of h by shifting to the left by 3 units. Therefore, if the x-intercept of h is at (0, 0), the x-intercept of g will be at:

$x = 0 - 3 = -3$

From the graph, the axis of symmetry appears to be at the line y = 2. Thus, we can equate:

$t + 1 = 2$ Solving this gives: $t = 1$

Starting with the inequality:

$-2 < \frac{1}{x - 1} < 0$ We can consider each part separately. For the left inequality:

$-2(x - 1) < 1 \Rightarrow -2x + 2 < 1 \Rightarrow -2x < -1 \Rightarrow x > \frac{1}{2}$ For the right inequality, we find values of x where \frac{1}{x - 1} is negative, which occurs when:

$x - 1 < 0 \Rightarrow x < 1$ Combining these gives:

$\frac{1}{2} < x < 1$