Question

20. Write a function that transforms f = 27° + 4

in the following way:
vertical stretch by a factor of 5 and shift by 3 units.
a g(x) = 10(x+3)^6 + 20
c. g(x) = 10(x + 3) ^6 + 4
b. g(x) = 10x^6 + 7
d. g(x) = 10(x-3)^6 + 4

Answer 1

To perform a vertical stretch by a factor of 5 and shift by 3 units on the function f = 27° + 4, the correct function is g(x) = g(x) = 10(x + 3) ^6 + 4. (option c).

Step-by-step explanation:

To transform the function f=27°+4 with a vertical stretch by a factor of 5 and a shift by 3 units, we need to apply these operations to the standard form of the function g(x)=a(x−h) n+k,

where a is the vertical stretch factor,

h is the horizontal shift,

n is the exponent, and

k is the vertical shift.

In the given options:

Option a does not have the correct horizontal shift.

Option b lacks both the correct vertical stretch factor and the horizontal shift.

Option c correctly represents a vertical stretch by 5 (as 10 is 5 times 2) and a horizontal shift by 3.

Option d has the incorrect horizontal shift.

The correct transformation is achieved in option c g(x) = 10(x + 3) ^6 + 4 where the function is vertically stretched by a factor of 5 and shifted 3 units to the left.

By carefully analyzing the given options and applying the principles of function transformations, we identify option c as the accurate representation of the desired transformation for the given function.