Question

The function f(x) = ln x is transformed into the equation

f(x) = 3.7 ln x.
Fill in the correct responses in the blanks below.
f(x) = 3.7 ln x
parent function by a factor of

Answer 1

The function f(x) = ln x is scaled by a factor of 3.7 to transform it into the function f(x) = 3.7 ln x, which stretches the graph vertically by that factor.

Step-by-step explanation:

The transformation of the function f(x) = ln x into the function f(x) = 3.7 ln x involves scaling the parent function by a factor. In this case, the transformation indicates that the parent function has been scaled by a factor of 3.7. This means that the output of the natural logarithm function is multiplied by 3.7, which will stretch the graph vertically by a factor of 3.7. This property is based on the concept that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. In simpler terms, for any base number b, we can write b as eln b, and if we apply an exponent like 3.7 to b, it multiplies the natural logarithm of b by that exponent.