What are the steps to performing the following transformation and then graphing it?
Transformation: Stretch f(x) = |2x| - 3 horizontally by a factor of 3/2.
g(x) = f(x/(3/2)) = f(2/3 x) = |2/3 * 2x| - 3 = |4x/3| - 3
See
http://www.wolframalpha.com/input/?i=plot+y%3D|2x|-3%2C+y%3D|4x%2F3|+-+3
To perform the transformation of stretching the function f(x) = |2x| - 3 horizontally by a factor of 3/2, the following steps can be followed:
Step 1: Start with the parent function f(x) = |x|. This is the basic function we will be working with.
Step 2: Determine the direction of the stretch. Since we are stretching the function horizontally, it means the x-values will be affected and the y-values will remain unchanged.
Step 3: Determine the factor of the stretch. In this case, the factor is 3/2. This means that every x-value will be multiplied by 3/2 to achieve the stretched function.
Step 4: Apply the transformation to the function. Multiply the x-values of the parent function by 3/2.
The equation of the stretched function is now f(x) = |(3/2)x| - 3.
To graph the stretched function, follow the steps below:
Step 5: Plot some points on the graph by substituting different x-values into the equation of the stretched function and calculating the corresponding y-values.
For example, let's choose a few x-values: -2, -1, 0, 1, 2.
Substituting these x-values into the equation f(x) = |(3/2)x| - 3, we can calculate the corresponding y-values. For each x-value, calculate the expression inside the absolute value first, then subtract 3 to find the y-value.
(-2) => |(3/2)(-2)| - 3 = 6/2 - 3 = 3 - 3 = 0
(-1) => |(3/2)(-1)| - 3 = 3/2 - 3 = -3/2
(0) => |(3/2)(0)| - 3 = 0 - 3 = -3
(1) => |(3/2)(1)| - 3 = 3/2 - 3 = -3/2
(2) => |(3/2)(2)| - 3 = 6/2 - 3 = 3 - 3 = 0
Step 6: Plot the points on a coordinate plane. The x-values should be plotted along the x-axis, and the corresponding y-values should be plotted along the y-axis.
(-2, 0), (-1, -3/2), (0, -3), (1, -3/2), (2, 0)
Step 7: Connect the plotted points with a smooth curve. Since we are working with the absolute value function, the graph will be V-shaped with the vertex at the point (0, -3).
This is how the stretched function f(x) = |(3/2)x| - 3 can be graphed after performing the transformation.