Transformations of exponential functions LO Sketch translations reflections

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Transformations of exponential functions LO: Sketch translations, reflections and stretches of exponential function

Transformations of exponential functions LO: Sketch translations, reflections and stretches of exponential function

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). Sketch: g(x) = f(x + 2) g(x) = 2 x + 2 f(x + 2) Move f(x) two units to the left hand side The y-intersection is translated to (-2, 1) (0, 1) f(x)

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). Sketch: h(x) = f(x – 3) h(x) = 2 x - 3 f(x + 2) f(x) Move f(x) three units to the right hand side The y-intersection is translated to (3, 1) (0, 1) (3, 1) f(x - 3)

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). In general f(x + 2) f(x + k) f(x) is translated k units to the left hand side f(x - k) f(x) is translated k units to the right hand side f(x) f(x - 3)

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). Sketch: g(x) = f(x) + 2 g(x) = 2 x + 2 f(x) Move f(x) two units upward The y-intersection is translated to (0, 3) f(x) + 2 (0, 3) (0, 1)

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). Sketch: h(x) = f(x) – 1 h(x) = 2 x - 1 Move f(x) one unit downward The y-intersection is translated to (0, 0) f(x) + 2 f(x) - 1 (0, 1) (0, 0)

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). In general f(x) + k f(x) is translated k units upward f(x) - k f(x) is translated k units downward f(x) + 2 f(x) - 1

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). Sketch: g(x) = -f(x) g(x) = -(2 x) f(x) Reflect f(x) over the x-axis -f(x)

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). Sketch: h(x) = f(-x) h(x) = 2 -x f(x) Reflect f(x) over the y-axis f(-x) -f(x)

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). In general -f(x) f(-x) f(x) is reflected over the x-axis f(x) f(-x) f(x) is reflected over the y -axis -f(x)

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). Sketch: g(x) = 2 f(x) = 2(2 x) Stretches f(x) vertically with scale factor 2 2 f(x)

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x

Simple transformations The diagram shows a sketch of the curve f(x) = 2 x which passes through the point A(0, 1). Sketch: g(x) = f(2 x) f(x) = 22 x f(2 x) f(x)