Question

Graph the function. Describe its position relative to the graph of the indicated function

Answer 1

To graph the function, we first need to know what means:

`f(x)=2^(x) +2` relative to
`f(x)=2^(x)`

This is called translation of functions, and it refers to the movement of a specific function, either upwards, downwards, leftwards or rightwards. To be able to translate a function, we have to use the next rules.

Moving upwards or downwards.

• If we sum a number to the whole function, we are gonna move that function upwards. For example, if we have
  `f(x)=x^(2)` and sum 3 to it, we would have
  `f(x)=x^(2) +3`, which is the same function but moved 3 units upwards.

• If we subtract a number to the whole function, we are gonna move that function downwards. For example, if we have
  `f(x)=x^(2)` and subtract 3 from it, we would have
  `f(x)=x^(2) -3`, which is the same function but moved 3 units downwards.

In this case, the problem is saying that we have to move the function upwards by two units, because
`f(x)=2^(x) +2` is the same function as
`f(x)=2^(x)`, but moved 2 units upwards.

In addition, the graph is attached, there you can see the difference between those two functions, you will se that they are the same, but one is moved two units upwards.

Answer 2

C

Explanation:

If the parent function is function
`y=f(x)` and
`a>0,` then

• the graph of the function
  `y=f(x-a)` is translated a units to the right graph of the parent function;
• the graph of the function
  `y=f(x+a)` is translated a units to the left graph of the parent function;
• the graph of the function
  `y=f(x)+a` is translated a units up graph of the parent function;
• the graph of the function
  `y=f(x)-a` is translated a units down graph of the parent function.

In your case, the grapgh of the function
`y=2^x+2` is translated 2 units up the graph of the function
`y=2^x.`