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2.9 Even and odd functions. Definition: A function, y = f(x), is even if f(x) = f( x) for all x in the domain of f. −. Geometrically, an even function is symmetrical about the y-axis (it has line symmetry). The function f(x) = x2 is an even function as f( x) = ( x)2 = x2 = f(x) for all values. − −.
Transformations of Functions (Advanced) Notes, Examples, and Practice Questions (with solutions) Topics include shifts, stretches, reflections, graphing, odd/even, domain/range, and more.
The diagram above shows a sketch of the curve with equation y = f(x), −1 ≤ x ≤ 3. The curve touches the x-axis at the origin O, crosses the x-axis at the point A(2, 0) and has a
Use transformations to graph the following functions: a) h(x) = −3 (x + 5)2 – 4 b) g(x) = 2 cos (−x + 90°) + 8 Solutions: a) The parent function is f(x) = x2 The following transformations have been applied: a = −3 (Vertical stretch by a factor of 3 and reflection in the x-axis) h = −5 (Translation 5 units to the left)
Graphs, Relations, Domain, and Range. The rectangular coordinate system1 consists of two real number lines that intersect at a right angle. The horizontal number line is called the x-axis2, and the vertical number line is called the y-axis3.
The graph of p is the graph of the parent function fl ipped over the x-axis. So, the graph of p ( x ) = − x 2 is a refl ection in the x -axis of the graph of the parent quadratic function.
VCE Maths Methods - Unit 3 - Transformation of functions Dilations (from the x axis) 4 • Dilations are multiplications that stretch the graph away from an axis. • Dilations can be from the from the x or y axis. • A dilation of a = 3 from the x axis: stretches vertically by a factor of 3. x'=x x=x' y'=a×y y= y' a y' a =(x')2 y'=a(x')2
