Let g(x) be the indicated combined transformation of f(x) = x. Write the rule for g(x).
Horizontal stretch by a factor of 5 followed by a horizontal shift 2 units.
Assuming a shift to the right, that would be
g(x) = (x-2)^2/5
See
http://www.wolframalpha.com/input/?i=plot+y+%3Dx^2%2C+y%3D%28x-2%29^2%2F5+for+-3%3C%3Dx%3C%3D5
To find the rule for g(x), which is the combination of a horizontal stretch by a factor of 5 followed by a horizontal shift of 2 units, we can break down the steps involved.
1. Start with the function f(x) = x.
2. Apply the horizontal stretch by a factor of 5. This means multiplying the x-values by 1/5.
The function after the stretch becomes f(x) = (1/5)x.
3. Next, apply the horizontal shift of 2 units. This means adding 2 to the x-values.
The function after the shift becomes g(x) = (1/5)x + 2.
Therefore, the rule for g(x) is g(x) = (1/5)x + 2.