Curriculum placement
Algebra 2. This describes the skill, not a learner estimate.
Shifts, stretches, and reflections of graphs
Describe shifts scales reflections and symmetry of functions
Problem types
- Classify a function as even, odd or neither
- Graph a square root function by placing points
- Equations of transformed graphs
- Where a point goes
- Features of a shifted polynomial
- Choose the graph of a quadratic or exponential rule
- Choose the graph of a shifted graph
- Write the rule of a shifted function
Builds on
- Piecewise and absolute-value functions
- Graphs of quadratic functions
- Solving absolute-value equations · Earlier idea
The graph of an absolute value equation is a V-shape shifted by the transformation of the expression inside.
Leads to
- Period, amplitude, and midline
- Logarithms as inverses of exponentials · See it applied
The graph of a logarithm is shifted, stretched and reflected by the same transformations.
Related skills
- Equations with one square root · Related idea
The graph of a square root equation is the root function shifted and stretched, so solving it reads where the shifted graph meets a line.
- Matrices as transformations of the plane · Related idea
Shifts, stretches and reflections of a graph are transformations, and matrices carry out such transformations on points.
- A parabola as points equally far from a focus and a line · Related idea
A parabola with its focus and directrix moved is the same locus, shifted, which the transformations of y = x squared describe.
- Constructing the image of a figure · Related idea
A sequence of translations, reflections and dilations carries one figure to another, as a sequence of shifts, reflections and stretches carries one graph to another.
- Parallel lines, perpendicular lines, and symmetry · Related idea
A graph symmetric about the y-axis has a line of symmetry, and this is what makes a function even.
Open the interactive map to explore lessons and skill connections.