Applying a horizontal stretch by a factor of p where p is a

Applying a horizontal stretch by a factor of p (where p is a constant such that p>1 ) to h(x)=lnx is equivalent to applying what shift to h? Give both the direction and the amount of the shift (in terms of p).

This is equivalent to applying a shift (left, right, up, or down) by ________ units.

Solution

We have given,

h(x) = ln x

Now if we apply a horizonatal streach of p units then the parent function h(x) will become:-

h(x) = ln(x/p)........................1

We have a logarithim rule called quotient rule ln(a/b) = lna – lnb

Use this rule in equation 1 we get,

h(x) = lnx – lnp

Now this is equivalent to shifting the parent function h(x) = lnx by lnp units downward.

So this is equivalent to applying a shift of lnp units downward.