The function g(x) = 2^x. the function f(x) = 2^x+k and k < 0. which of the following statements is true? a) the graph of f(x) is shifted k units to the left of the graph of g(x). b) the graph of f(x) is shifted k units to the right of the graph of g(x). c) the graph of f(x) is shifted k units above the graph of g(x). d) the graph of f(x) is shifted k units below the graph of g(x).

Option D)

Step-by-step explanation:

If the graph of the function  represents the transformations made to the graph of  then, by definition:

If  the graph moves vertically b units up

If the graph moves vertically b units down

If  the graph moves horizontally h units to the left

If the graph moves horizontally h units to the rigth

In this problem we have the function and our parent function is

therefore it is true that  and

Then "The graph of f(x) is shifted k units below the graph of g(x)".

The answer is Option D)

_________________________________________________

Note:

If the function are:

Then and . This means that the function f(x) shifts k units to the right of the function g(x)

And the answer would be the option B)

B) The graph of f(x) is shifted k units to the right of the graph of g(x).

Step-by-step explanation:

We given the functions and where .

We know that horizontal depends on the value of x and are when

when graph is shifted to left; and

when graph is shifted to right.

Given the above functions, when k is considered positive then f(x) becomes .

Therefore, the graph of f(x) is shifted k units to the right of the graph of g(x).

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|