The curve has a turning point at A(3, 4) − and also passes through the point (0, 5).
(a) Write down the coordinates of the point to which A is transformed on the curve with equation
(i) y = |f(x)| ,
(ii) y = 2f(1/2x)
(b) Sketch the curve with equation y = f(|x|)
On your sketch show the coordinates of all turning points and the coordinates of the point at which the curve cuts the y-axis.
The curve with equation y = f(x) is a translation of the curve with equation y = x2
(c) Find f(x).
(d) Explain why the function f does not have an inverse.
Give the value of α to 4 decimal places.
(b) (i) Find the maximum value of 2 sin θ – 1.5 cos θ.
(ii) Find the value of θ, for 0 ≤ θ < π, at which this maximum occurs.
Tom models the height of sea water, H metres, on a particular day by the equation
H = 6 + 2 sin (4πt/25) - 1.5 cos (4πt/25), 0 ≤ t < 12
where t hours is the number of hours after midday.
(c) Calculate the maximum value of H predicted by this model and the value of t, to 2 decimal places, when this maximum occurs.
(d) Calculate, to the nearest minute, the times when the height of sea water is predicted, by this model, to be 7 metres.
ln(2x2 + 9x - 5) = 1 + ln (x2 + 2x - 15), x ≠ -05
(b) find x in terms of e.
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