Starting with the graph of f(x)=7x, write the formula for the function that results from e (a) shifting f(x) 8 units to the right. y= ? (b) reflecting f(x) about the x-axis and the y-axis. y=?

Question

Starting with the graph of f(x)=7^x, write the formula for the function that results from

e

(a) shifting f(x) 8 units to the right. y= ?

(b) reflecting f(x) about the x-axis and the y-axis. y=?   

Thank you,

[3.5A_8]

Answer 1

f(x) = 7x = 7

shift it right 8

leaves f(x) = y = 7(x-8) = 7x -56

reflect f(x) = 7x about the x axis

changes y to -y

e(x) = -7x

reflect over the y axis

changes x to -x

e(x) becomes 7x = f(x)

back to where you started

unless you did the reflectios after the shift right

then

e(x) becomes after the x reflection, switching y with -y, -y = 7(x-7) or y = 7(7-x)

then after a y reflection

e(x) becomes, after switching x with -x, y =7(7+x) = 49+7x

e(x) = 49+7x

WHOOPs, you have y=7x in the intial post but y=7^x in the 2nd

that changes things a bit

shift x right 7 changes f(x)= 7^x to e(x) = 7^(x-7)

then do an x reflection to switch y to -y

-y = 7^(x-7) or y= e(x) = -7^(x-7)

then a y axis reflection, switching x with -x

y = -7^(-x-7) = e(x)

shift right by a units changes x to x-a

reflect over the x axis switches y to -y

reflect over y axis changes x to -x