In this video lesson we will learn how to describe horizontal stretches and shrinks, as well as, vertical stretches and shrinks. We will learn that horizontal stretches and shrinks multiply each input by a factor and the function and its transformation will always have the same y-intercept. The scale factor of a horizontal stretch or shrink is the reciprocal of a. We will learn that vertical stretches and shrinks multiply each output by a factor and the function and its transformation will have the same x-intercept. The scale factor of a vertical stretch or shrink is the factor a. We will learn how to describe these transformations from function notation and graph the transformations. Student practice is embedded in the lesson with modeled exemplar solutions.
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00:00 Introduction
00:37 Horizontal Stretches & Shrinks Facts
01:58 Vertical Stretches & Shrinks Facts
03:03 Graphs of Vertical Stretches & Shrinks
03:48 Using a Table to Graph a Stretch or Shrink
05:56 Student Practice #1
07:16 Student Practice #2
08:33 Student Practice #3
Common Core Math Standards
Analyze functions using different representations.
HS.F.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
HS.F.IF.C.7.A Graph linear and quadratic functions and show intercepts, maxima, and minima.
Build new functions from existing functions.
HS.F.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
