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What is the range of f(x) = (three-fourths) Superscript x – 4?

y > –4



Left-brace y vertical line y greater-than three-fourths right-brace



y < –4



Left-brace y vertical line y less-than three-fourths right-brace

2 Answers

5 votes

Answer:

Option 1 -
\y>-4\

Explanation:

Given : Function
f(x)=((3)/(4))^x-4

To find : What is the range of f(x) ?

Solution :

Function
f(x)=((3)/(4))^x-4

We put some value of x to determine the range,

For x=-1,


f(0)=((3)/(4))^(-1)-4=0.33

For x=0,


f(0)=((3)/(4))^0-4=-4

For x=1,


f(0)=((3)/(4))^1-4=-0.25

For x=2,


f(0)=((3)/(4))^2-4=-0.4375

As we see that, the value of y is greater than -4.

Therefore, the range of the function is
\y>-4\

So, Option 1 is correct.

User Assaf Shomer
by
6.1k points
5 votes

Answer:

Option A.

Explanation:

The given function is


f(x)=(3)/(4)^(x)-4

We need to find the range of f(x).

The given function can be rewritten as


y=(3)/(4)^(x)-4

Range is the set of output values.

If
a^x, where a>0, then the value of
a^x is always greater than 0.

Using the above property, we get


(3)/(4)^(x)>0

Subtract 4 from both sides.


(3)/(4)^(x)-4>0-4


y>-4

Range = y

Therefore, the correct option is A.

User Rouan Van Dalen
by
5.6k points