Review practice · Section 1 of 2

The given graph is $y=f(2x)$, passing through A=(−1,0), B=(0,2), C=(1,0), D=(3,−3). The diagram shows a right-hand horizontal asymptote y=−1.

Sketch on separate clearly labelled diagrams:

(i) $y=f(-2x)$;1 mark

(ii) $y=f(2-2x)$;2 marks

(iii) $y=\frac12f(2x)$.2 marks

The given graph is $y=f(x)$, with maximum A=(2,2), B=(4,0), C=(0,1) and vertical asymptote x=5; its left tail approaches y=0. Sketch on separate diagrams:

(i) $y=f(2x-1)$;3 marks

(ii) $y=f(x/2)-2$;3 marks

(iii) $y=1/f(x)$;4 marks

Show the corresponding A,B,C coordinates and all asymptotes where applicable.

The given graph $y=f(x)$ intersects the axes at A=(0,−2), B=(−1,0), has minimum C=(4,0.5), and asymptotes x=1, y=3.

Sketch separately:

(i) $y=f(-1-x)$;4 marks

(ii) $y=1/f(x)$;4 marks

Clearly indicate asymptotes, axial intercepts and corresponding A,B,C where appropriate.

(a) $y=x^2-1$ is translated 3 units in the positive x-direction, stretched by factor 2 parallel to y, then translated 2 units in the negative y-direction. Find the new equation as $y=f(x)$.3 marks

(b) Three successive transformations change $y=h(x)$ to $y=h(1-2x)$. Describe them.3 marks

The given graph $y=f(x)$ has asymptotes $x=-1$, $y=-2$, turning point $A=(1,3)$, and zeros $O=(0,0)$, $B=(-2,0)$, $C=(4,0)$.

(a) State the turning point of $y=1+\frac13f(x)$.1 mark

(b) Sketch $y=|f(x)|$, labelling asymptotes and the points corresponding to A,B,C.2 marks

(c) Sketch $y=-f(2x)$ with those labels.3 marks

(d) Sketch $y=1/f(x)$, labelling asymptotes, turning points and axis crossings.3 marks

A reflects in the y-axis; B translates 4 units in the positive x-direction; C scales parallel to y by 2. A curve undergoes A,B,C in that order, giving $y^2=-4x$. Determine its equation before the transformations.3 marks