Respuesta :
Answer:
The range is [tex](0,\infty)[/tex] (in interval notation).
The range is [tex]0<y<\infty)[/tex] or [tex]y>0[/tex] (in inequality notation).
The range is all real numbers greater than 0 (in words).
Step-by-step explanation:
[tex]5^{x}[/tex] we get close to 0 but will never be 0. [tex]5^{x}[/tex] will also never be negative.
[tex]5^{x}[/tex] is positive for any real input [tex]x[/tex].
Here is a table of values to help try to convince you we are only ever going to get positive outcomes.
[tex]x[/tex] | [tex]5^x[/tex]
-4 5^(-4)=1/625
-3 5^(-3)=1/125
-2 5^(-2)=1/25
-1 5^(-1)=1/5
0 5^0=1
1 5^1=5
2 5^2=25
3 5^3=125
4 5^4=625
You can see the y's are increasing as you increase the x value.
Even if you plug in really left numbers on the number like -200 you will still get a positive number like [tex]5^{-200}=\frac{1}{5^{200}}[/tex]. This number will be really close to 0. You can go more left of -200 and the outcome will be even closer to 0.
I'm just trying to convince you on the left side the y's will approach 0 but never cross the x-axis on the right side the numbers keep getting larger and larger.
The range is [tex](0,\infty)[/tex] (in interval notation).
The range is [tex]0<y<\infty)[/tex] or [tex]y>0[/tex] (in inequality notation).
The range is all real numbers greater than 0 (in words).
You can also look at the graph and see that the y's for this equation only exist for number y's greater than 0. You only see the graph above the x-axis.
Answer:
The range is f(x) = all real values above 0.
In interval notation it is (0, ∞).
Step-by-step explanation:
5^x can have any value above 0 . It cannot be negative or 0.
