IB Math · Topic practice · IB Mathematics AA SL · Unit 2
Functions A mixed exercise set, like a textbook: every problem type this unit covers, shuffled together and getting harder as you go. Work on paper, reveal to check — and hit
All levels Level 1 · Basics Level 2 · Standard Level 3 · Exam
1. Let f ( x ) = 2 x + 1 f(x) = 2x + 1 f ( x ) = 2 x + 1 and g ( x ) = x 2 + 2 g(x) = x^2 + 2 g ( x ) = x 2 + 2 . Find ( f ∘ g ) ( 3 ) (f \circ g)(3) ( f ∘ g ) ( 3 ) .
2. Let f ( x ) = 2 x + 1 f(x) = 2x + 1 f ( x ) = 2 x + 1 . Find f − 1 ( 5 ) f^{-1}(5) f − 1 ( 5 ) .
3. The graph of f ( x ) = x 2 − 2 x + 3 f(x) = x^2 - 2x + 3 f ( x ) = x 2 − 2 x + 3 has its vertex at the point:
4. How many real roots does x 2 − 9 x − 6 = 0 x^2 - 9x - 6 = 0 x 2 − 9 x − 6 = 0 have?
5. The function f ( x ) = x + 1 x + 2 f(x) = \dfrac{x + 1}{x + 2} f ( x ) = x + 2 x + 1 has asymptotes:
6. The point ( 2 , 3 ) (2,\ 3) ( 2 , 3 ) lies on the graph of y = f ( x ) y = f(x) y = f ( x ) . Find the image of this point on the graph of y = 2 f ( x − 1 ) + 1 y = 2f(x - 1) + 1 y = 2 f ( x − 1 ) + 1 .
7. Let f ( x ) = 2 x − 3 f(x) = 2x - 3 f ( x ) = 2 x − 3 and g ( x ) = x 2 + 3 g(x) = x^2 + 3 g ( x ) = x 2 + 3 . Find ( f ∘ g ) ( 1 ) (f \circ g)(1) ( f ∘ g ) ( 1 ) .
8. Let f ( x ) = 3 x + 1 f(x) = 3x + 1 f ( x ) = 3 x + 1 . Find f − 1 ( 10 ) f^{-1}(10) f − 1 ( 10 ) .
9. The graph of f ( x ) = x 2 − 6 x + 13 f(x) = x^2 - 6x + 13 f ( x ) = x 2 − 6 x + 13 has its vertex at the point:
10. How many real roots does x 2 − 8 x − 5 = 0 x^2 - 8x - 5 = 0 x 2 − 8 x − 5 = 0 have?
11. The function f ( x ) = x + 5 x − 4 f(x) = \dfrac{x + 5}{x - 4} f ( x ) = x − 4 x + 5 has asymptotes:
12. The point ( − 1 , 4 ) (-1,\ 4) ( − 1 , 4 ) lies on the graph of y = f ( x ) y = f(x) y = f ( x ) . Find the image of this point on the graph of y = 2 f ( x − 1 ) − 4 y = 2f(x - 1) - 4 y = 2 f ( x − 1 ) − 4 .
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