Question

A function, f(x) = x, is vertically translated 4 units up and then reflected across the y-axis. What's the new function in terms of g(x)?

Answer 1

Answer:

The new function is g(x) = -x + 4

Step-by-step explanation:

• If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k

• If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

∵ A function f(x) = x

∵ It is vertically translated 4 units up

→ By using the 1st rule above, the value of k = 4

∴ k = 4

∵ Its image h(x) = f(x) + k

∴ Its image h(x) = f(x) + 4

∴ Its image h(x) = x + 4

∵ Then it is reflected across the y-axis

→ By using the 2nd rule above, change the sign of x in h(x)

∵ h(x) = x + 4

∴ g(x) = h(-x)

∴ g(x) = -x + 4

∴ The new function is g(x) = -x + 4