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Teacher Name: Jose Ramirez
Grade: 9
Subject: Algebra I
TN State Standard: A1.F.BF.B.2 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 graphs.
Learning Objective: Students will interpret the effects of functions by shifting, reflecting, compressing, or stretching vertically or horizontally.
Recall that the parent functions are the functions before they are transformed. In other words, they are the simplest form. Some examples are:
y=x (Linear)
y=abs(x) (Absolute Value)
y=x^2 (Quadratic)
Let's take a look at the parent function y=abs(x) and its transformed function y=-2abs(x-3)+5
There are 4 transformations involved: reflection, vertical stretch, horizontal shift, and vertical shift.
The order of these effects is done by the order of operations.
So, a shift of 3 units to the right followed by a reflection over the x-axis. Then, stretch vertically by a factor of 2. Finally, shift 5 units up.
Graphical representation with Desmos
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