Which functions represent a horizontal translation to the left of the parent function f(x) = ln x?

check all that apply.

g(x) = 3 ln(x − 1) + 6
h(x) = 3 ln(x + 3) + 1
r(x) = −3 ln(x + 1) + 3
s(x) = −3 ln(x) − 3
p(x) = ln(x + 2) − 2

A horizontal shift happens when you add or subtract a value from the input value of x.

To shift left the number would be added to the x.

The answers are:

h(x) = 3 ln(x + 3) + 1

r(x) = −3 ln(x + 1) + 3

p(x) = ln(x + 2) − 2

h(x) = 3 ln(x + 3) + 1

r(x) = −3 ln(x + 1) + 3

p(x) = ln(x + 2) − 2

Step-by-step explanation:

The parent function given to us is: .

A horizontal translation to the left k units is of the form .

This implies that;

h(x) = 3 ln(x + 3) + 1, is a horizontal translation to the left by 3 units.

r(x) = −3 ln(x + 1) + 3, is a horizontal translation to the left by 1 unit.

p(x) = ln(x + 2) − 2, is a horizontal translation to the left by 2 unit.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

it shoild be o

step-by-step explanation: