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Transforming functions: horizontal shifts 

Grade 12 Math: Master Advanced Concepts & Skills

Geometric constructions

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Classifying triangles

Isosceles and equilateral triangles

Conics - Parabola

Conics - Circle

Conics - Ellipse

Conics - Hyperbola

Parallel and perpendicular lines

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Circle geometry

Angles in a circle

Circles and circumference

Circle properties

Arcs of a circle

Areas and sectors of circles

Transformations of 2D shapes

Line symmetry

Rotational symmetry and transformations

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Non-Euclidean geometries

Combining transformations of functions

Surface area of 3-dimensional shapes

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

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Geometry 12

math

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Ex. 1:

Ex. 2:

Horizontal translations refer to movements of a graph of a function horizontally along the x-axis by changing the x values. So, if y = f(x), then y = (x &ndash;h) results in a horizontal shift. If h > 0, then the graph shifts h units to the right; while If h < 0, then the graph shifts h units to the left.

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula