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)?

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

Step-by-step explanation:

∵ 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

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5