Graphs and transformations 4G
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1 Graphs and transformations 4G a f(x + ) is a translation by one unit to the left. d A (0, ), B ( ),0, C (, 4), D (, 0) A (, ), B (0, 0), C (, 4), D (5, 0) e f(x) is a stretch with scale factor b f(x) 4 is a translation by four units down. 4 A (0, 6), B (, 0), C (4, ), D (6, 0) A (0, ), B (, 4), C (4, 0), D (6, 4) f f( ) x is a stretch with scale factor c f(x + 4) is a translation by four units to the left. 4 A (0, ), B (, 0), C (8, 4), D (, 0) g f(x) is a stretch with scale factor A ( 4, ), B (, 0), C (0, 4), D (, 0) d f(x) is a stretch with scale factor A (0, ), B (, 0), C (4, ), D (6, 0) Pearson Education Ltd 07. Copying permitted for purchasing institution only. This material is not copyright free.
2 h f( x) is a reflection y-axis c f(x) is a stretch with scale factor A (0, ), B (, 0), C ( 4, 4), D ( 6, 0) a f(x) + is a translation by two units up. The horizontal asymptote is y = 4. The vertical asymptote is x =. d f(x) is a translation by two units down. The curve crosses the x-axis at (0, ) and the y-axis at (a, 0), where 0 < a <. The horizontal asymptote is y = 4. The vertical asymptote is x =. b f(x + ) is a translation by one unit to the left. The curve crosses the y-axis at (0, ). The vertical asymptote is x =. e f(x) is a stretch with scale factor The curve crosses the x-axis at (, 0). The horizontal asymptote is y =. The vertical asymptote is x = 0. The horizontal asymptote is y =. The vertical asymptote is x =. Pearson Education Ltd 07. Copying permitted for purchasing institution only. This material is not copyright free.
3 f f ( ) x is a stretch with scale factor a f(x ) is a translation by two units to the right. 0 The horizontal asymptote is y =. The vertical asymptote is x =. g f(x) is a stretch with scale factor A (, 6), B (0, 0), C (, ), D (6, 0) b f(x) + 6 is a translation by 6 six units up. A ( 4, 0), B (, 6), C (0, ), D (4, 6) The horizontal asymptote is y =. The vertical asymptote is x =. h f(x) is a reflection x-axis. c f(x) is a stretch with scale factor A (, 6), B (, 0), C (0, ), D (, 0) The horizontal asymptote is y =. The vertical asymptote is x =. Pearson Education Ltd 07. Copying permitted for purchasing institution only. This material is not copyright free.
4 4 d f(x + 4) is a translation by four units to the left. g f(x) is a stretch with scale factor A ( 4, ), B (, 0), C (0, ), D (4, 0) A ( 8, 6), B ( 6, 0), C ( 4, ), D (0, 0) e f(x) + is a translation by three units up. h f( ) 4 x is a stretch with scale factor 4 A ( 6, 6), B ( 8, 0), C (0, ), D (6, 0) A ( 4, ), B (, ), C (0, 0), D (4, ) i f(x) is a reflection x-axis. f f(x) is a stretch with scale factor A ( 4, 6), B (, 0), C (0, ), D (4, 0) j f( x) is a reflection y-axis. A ( 4, 8), B (, 0), C (0, 9), D (4, 0) A (4, 6), B (, 0), C (0, ), D ( 4, 0) Pearson Education Ltd 07. Copying permitted for purchasing institution only. This material is not copyright free. 4
5 4 a i f(x) is a stretch with scale factor in the iv f(x) is a translation by one unit down. The curve crosses the y-axis at (0, ). The vertical asymptote is x =. ii f(x) is a stretch with scale factor in the The horizontal asymptote is y =. The vertical asymptote is x =. v f( x) is a reflection y-axis. The curve crosses the y-axis at (0, ). The vertical asymptote is x =. iii f(x ) is a translation by two units to the right. 0 The curve crosses the y-axis at (0, ). The vertical asymptote is x =. vi f(x) is a reflection x-axis. There are no intersections with the axes. The vertical asymptote is x = 0. The curve crosses the y-axis at (0, ). The vertical asymptote is x =. Pearson Education Ltd 07. Copying permitted for purchasing institution only. This material is not copyright free. 5
6 4 b The shape of the curve is like y = k x, k > 0. x = asymptote suggests denominator is zero when x =, so denominator is x +. Also, f(0) = means the numerator must be. f(x) = x + 5 a P(, ) is mapped to Q(4, ). The x-coordinate has doubled, which is a stretch with scale factor y = f ( x ) a = b i f(x 4) is a translation by four units to the right. So P is mapped to (6, ). 4 0 ii f(x) is a stretch with scale factor in the So P is mapped to (, ). 6 b y = f(x) y = f(x), which is a stretch with scale factor A (, 0), B (0, 4), C (, 4), D (, 0) c y = f(x) y = f(x) +, which is a translation by three units up. iii f(x) 4 is a stretch with scale factor y-direction and then a translation by four units down. 4 So P is mapped to (, ) 6 a y + = f(x) y = f(x), which is a translation by two units down. A (, ), B (0, 5), C (, 5), D (, ) d y = f(x) y = f(x), which is a stretch with scale factor A (, ), B (0, 0), C (, 0), D (, ) A (, 0), B ( ) 0,, C (, ), D (, 0) Pearson Education Ltd 07. Copying permitted for purchasing institution only. This material is not copyright free. 6
7 6 e y = f(x) y = f(x) +, which is a stretch with scale factor y-direction, then a translation by, or unit up. A (, ), B ( ) D (, ) 0,, C (, ), Pearson Education Ltd 07. Copying permitted for purchasing institution only. This material is not copyright free. 7
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