Question

Consider function f below.

$f(x)=4^{x} -6$

Determine function g which is created by shifting the graph of function f up 5 units.

A. g(x) = 4(x + 5) - 6
B. g(x) = 9x - 6
C. g(x) = 4x - 1
D. g(x) = 4x + 5

Answer 1

For this case we have a function of the form:

$f (x) = 4 ^ x-6$

We want to move the graph five units up.

Therefore, the new function is given by:

$g (x) = f (x) +5$

Substituting we have:

$g (x) = 4 ^ x-6 + 5$

Rewriting the function:

$g (x) = 4 ^ x-1$

Answer:

The new function is given by:

$g (x) = 4 ^ x-1$

option C

Answer 2

Answer:

Option C - $g(x)=4^{x} -1$

Step-by-step explanation:

Given : Function $f(x)=4^{x} -6$

To find : Determine function g which is created by shifting the graph of function f up 5 units?

Solution :

Shifting the graph upward in the function by some unit is defined as

f(x) → f(x)+b i.e. shifting upward by b unit.

Applying the transformation rule in the given function,

$f(x)=4^{x} -6$

Shifting upward by 5 unit i.e. f(x)+5

$g(x)=4^{x} -6+5$

$g(x)=4^{x} -1$

Therefore, The required function g is defined as $g(x)=4^{x} -1$ .

So, Option C is correct.