Unit 5
4 marks · EasyA function is defined as f(x) = x^2. The function is transformed by a translation of (−2, 0). The number x has been measured to the nearest integer and is given as 5.
Write down the equation of the transformed function.
What is the image of the point (5, 25) after this translation?
Write down the lower and upper bounds of x.
Calculate the lower bound of f(x) using your answer to part (c).
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) y = (x + 2)^2
(b) (3, 25)
(c) Lower bound = 4.5, Upper bound = 5.5
(d) f(4.5) = (4.5)^2 = 20.25
Common mistakes: Translation in wrong direction; Bounds incorrect (should be 4.5, 5.5); Incorrect calculation of f(4.5)
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Correct equation: y = (x + 2)^2.
A1 (b) · 1 mark · Correct image coordinates found after translation: (3, 25).
B1 (c) · 1 mark · Lower bound 4.5, upper bound 5.5 written down.
A1 (d) · 1 mark · Calculation of f(4.5) = 20.25.
Worked solution
(a) The translation (−2, 0) means shifting two units to the left: y = (x + 2)^2
(b) After x translation: (5, 25) → (3, 25)
(c) Lower bound of x is 5 - 0.5 = 4.5, upper bound is 5 + 0.5 = 5.5.
(d) f(4.5) = (4.5)^2 = 20.25