Respuesta :
Answer:
Option 1 - [tex]\{y|y>-4\}[/tex]
Step-by-step explanation:
Given : Function [tex]f(x)=(\frac{3}{4})^x-4[/tex]
To find : What is the range of f(x) ?
Solution :
Function [tex]f(x)=(\frac{3}{4})^x-4[/tex]
We put some value of x to determine the range,
For x=-1,
[tex]f(0)=(\frac{3}{4})^{-1}-4=0.33[/tex]
For x=0,
[tex]f(0)=(\frac{3}{4})^0-4=-4[/tex]
For x=1,
[tex]f(0)=(\frac{3}{4})^1-4=-0.25[/tex]
For x=2,
[tex]f(0)=(\frac{3}{4})^2-4=-0.4375[/tex]
As we see that, the value of y is greater than -4.
Therefore, the range of the function is [tex]\{y|y>-4\}[/tex]
So, Option 1 is correct.
Answer:
Option A.
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{3}{4}^{x}-4[/tex]
We need to find the range of f(x).
The given function can be rewritten as
[tex]y=\frac{3}{4}^{x}-4[/tex]
Range is the set of output values.
If [tex]a^x[/tex], where a>0, then the value of [tex]a^x[/tex] is always greater than 0.
Using the above property, we get
[tex]\frac{3}{4}^{x}>0[/tex]
Subtract 4 from both sides.
[tex]\frac{3}{4}^{x}-4>0-4[/tex]
[tex]y>-4[/tex]
Range = {y | y > –4}
Therefore, the correct option is A.
