Question

The red graph (1) is the graph of f(x) = log(x). Describe the transformation of the blue function (2) and write the equation of the graph.

Answer 1

reflection across the x-axis

Answer 2

and then a shift down

Answer 3

if you first reflect the red curve, the y=+1 on the right side of the curve becomes y=-1
then it looks like you shift down a little more to get to the blue curve.

Answer 4

so how many units down is the shift

Answer 5

3?

Answer 6

look at the point (10,1). multiply the y value by -1 to reflect the point
you get (10,-1)
the blue curve is at (10,-4)

so you shift down 3

Answer 7

yay that's what i thought

Answer 8

and there is no right/left shift.

Answer 9

correct. so how do i write in an equation that the graph reflected and shifted down 3 units

Answer 10

first multiply the original by -1, then add -3 to shift down (just like usual)

Answer 11

f (x) = log(-1) -3

is that right?

Answer 12

the -3 is ok
you start with f(x)= log(x)

if you make it f(x)= -log(x)
that will reflect it (the y values become negative)

Answer 13

gotcha, so f(x) = -log(x) -3 ?

Answer 14

yes

Answer 15

thank god. only one left!

Answer 16

btw, you can't take log of negative numbers

Answer 17

i think i knew that. hahaha

Answer 18

i'll open a new question