Practice — what type is this question? (Functions Graphs)

Below are the graphs of f(x) = x² + bx − 3 and g(x) = a/(x + p). • f has a turning point at C and passes through the x-axis at (1 ; 0). • D is the y-intercept of both f and g. The graphs f and g also intersect each other at E and J. • The vertical asymptote of g passes through the x-intercept of f. 4.1 Write down the value of p. 4.2 Show that a = 3 and b = 2.

Source: DBE Mathematics Paper 1, November 2019, Question 4.1–4.2

Given f(x) = x² + 2x − 3 (from QUESTION 4.1–4.2 above). The function h(x) = f(m − x) + q has only one x-intercept, at x = 0. Determine the values of m and q.

Source: DBE Mathematics Paper 1, November 2019, Question 4.7

Sketched below is the graph of f(x) = k^x (k > 0), passing through (4 ; 16). Graph g is obtained by reflecting f about the line y = x. 5.4.1 Use your graph to determine the value(s) of x for which f(x) × g(x) > 0.

Source: DBE Mathematics Paper 1, November 2019, Question 5.4.1