Question

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

Answer 1

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

r(x) = −3 ln(x + 1) + 3

p(x) = ln(x + 2) − 2

Explanation:

The parent function given to us is:
`f(x)=\ln x`.

A horizontal translation to the left k units is of the form
`y=\ln (x+k)`.

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.

Answer 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