Example Card: Reflections and Stretches
Apply reflections and stretches to function graphs in Grade 9 algebra: multiply by -1 to reflect across the x-axis, by values >1 to stretch vertically, and by 0<k<1 to compress.
Key Concepts
Now let's see what happens when we put a number in front. This relates to the key idea of reflections, stretches, and compressions.
Example Problem.
Describe the graph of the function $f(x) = 2|x|$.
Common Questions
How does multiplying a function by -1 transform its graph?
Multiplying f(x) by -1 gives -f(x), which reflects the graph across the x-axis. Every y-value becomes its opposite: points above the x-axis move below it, and vice versa.
What is the difference between a vertical stretch and compression?
For y = k·f(x), if k > 1, the graph stretches vertically (points move away from the x-axis). If 0 < k < 1, the graph compresses vertically (points move toward the x-axis). k = 2 doubles all y-values; k = 0.5 halves them.
How can a single equation produce both a reflection and a stretch?
A negative k value in y = k·f(x) combines both effects. For y = -3f(x), the 3 stretches the graph vertically by a factor of 3, and the negative sign reflects it across the x-axis simultaneously.