If the parent function of 𝑦=𝑥 is stretched by a factor of 2 and shifted right 4 units to transform into a new function, which of the following is the new function?
stretch by a factor of 2 : ----> y = 2x
shifted to the right 4 units
y = 2(x-4)
To stretch the parent function 𝑦=𝑥 by a factor of 2, we multiply the 𝑥-coordinate by 2. This results in the new function 𝑦=2𝑥.
To shift the new function 𝑦=2𝑥 right 4 units, we subtract 4 from the 𝑥-coordinate. Therefore, the new function becomes 𝑦=2(𝑥-4).
Hence, the new function is 𝑦=2(𝑥-4).
To transform the parent function 𝑦=𝑥, we can follow two steps: stretching and shifting.
1. Stretching: When the parent function is stretched by a factor of 𝑎, the equation becomes 𝑦=𝑎𝑥. In this case, the function is stretched by a factor of 2, so the equation becomes 𝑦=2𝑥.
2. Shifting: When the parent function is shifted right 𝑘 units, the equation becomes 𝑦=𝑥−𝑘. In this case, the function is shifted right 4 units, so the equation becomes 𝑦=2𝑥−4.
Therefore, the new function, after the stretch and shift, is 𝑦=2𝑥−4.