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
