Question

The parent function f(x) = log5x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it up three units. Which function is representative of this transformation?

Answer 1

Answer:

The function formed is g(x) -2log5x+3 .....

Step-by-step explanation:

According to the given statement the parent function f(x) = log5x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it up three units.

We have to find which function is representative of this transformation?

Solution:

The parent function y= log5x has been transformed by reflecting it over the x-axis.

f(x,y)⇒f(x,-y)

-y = log5x

y= -log5x

Now stretching it vertically by a factor of two means multiply the factor by output constant given.

y= -2log5x

Then shifting it up three units:

It means f(x)⇒f(x)+b function shift upwards by b units.

y= -2log5x+3

Thus the function formed is g(x) -2log5x+3 .....