HSC Exam Questions (Real Functions) 1995 HSC Q4(b) 4
(i) Draw the graphs of π¦ = |π₯| and π¦ = π₯ + 4 on the same set of axes.
(ii) Find the coordinates of the point of intersection of these two graphs.
1997 HSC Q4(b) 6
(i) Sketch the graph of π¦ = π₯! β 6 and label all intercepts with the axes.
(ii) On the same set of axes, carefully sketch the graph of π¦ = |π₯|.
(iii) Find the π₯ coordinates of the two points where the graphs intersect.
(iv) Hence solve the inequality π₯! β 6 β€ |π₯|.
2000 HSC Q1(g)
Sketch the line π¦ = 2π₯ + 3 in the Cartesian plane. 2
2001 HSC Q5(a)
State the domain and range of the function π¦ = 2 25 β π₯!. 3
2002 HSC Q6(a)
Sketch the graph of π¦ = 4 β π₯!, and state the range. 2
2003 HSC Q3(c)
Shade the region in the Cartesian plane for which the inequalities π¦ < π₯ β 2, π¦ β₯ 0 and π₯ β₯ 6
hold simultaneously. 2
2008 HSC Q8(a)
Let π π₯ = π₯! β 8π₯!.
(i) Find the coordinates of the points where the graph of π¦ = π(π₯) crosses the π₯ and π¦ axes.
1
(ii) Show that π(π₯) is an even function. 1
(iii) Sketch the graph of π¦ = π(π₯). 1
2009 HSC Q1(a)
Sketch the graph of π¦ β 2π₯ = 3, showing the intercepts on both axes. 2
2009 HSC Q3(c)
Shade the region in the plane defined by π¦ β₯ 0 and π¦ β€ 4 β π₯!. 2
2010 HSC Q1(c)
Write down the equation of the circle with centre (β1, 2) and radius 5. 1
2010 HSC Q1(g)
Let π π₯ = π₯ β 8. What is the domain of π(π₯)? 1
2010 HSC Q4(d)
Let π π₯ = 1 + π! .
Show that π π₯ Γπ βπ₯ = π π₯ + π(βπ₯). 2
2011 HSC Q4(e)
The diagram shows the graphs π¦ = π₯ β 2 and π¦ = 4 β π₯!. 2
Write down inequalities that together describe the shaded region.
2013 HSC Q3
Which inequality defines the domain of the function π π₯ = !!!!
?
(A) π₯ > β3
(B) π₯ β₯ β3
(C) π₯ < β3
(D) π₯ β€ β3
2013 HSC Q11(g)
Sketch the region defined by π₯ β 2 ! + π¦ β 3 ! β₯ 4. 3
2013 HSC Q15(c)
(i) Sketch the graph π¦ = |2π₯ β 3|. 1
(ii) Using the graph from part (i), or otherwise, find all values of π for which the equation
2π₯ β 3 = ππ₯ + 1 has exactly one solution. 2
2014 HSC Q2
Which graph best represents π¦ = π₯ β 1 !?
(A)
(B)
(C)
(D)