Answer:
Option D is the correct answer.
Explanation:
The points (0, 1), (1, 5), (2, 25), (3, 125) are on the graph of a function.
We need to find f(x)
Checking each options.
a) f(x) = [tex]2^x[/tex]
For (0,1)
f(0) = [tex]2^0=1[/tex]
For (1,5)
f(1) = [tex]2^1=2[/tex], given that f(1) = 5, so option A is wrong.
b) f(x) = [tex]3^x[/tex]
For (0,1)
f(0) = [tex]3^0=1[/tex]
For (1,5)
f(1) = [tex]2^1=3[/tex], given that f(1) = 5, so option B is wrong.
c) f(x) = [tex]4^x[/tex]
For (0,1)
f(0) = [tex]4^0=1[/tex]
For (1,5)
f(1) = [tex]4^1=4[/tex], given that f(1) = 5, so option C is wrong.
d) f(x) = [tex]5^x[/tex]
For (0,1)
f(0) = [tex]5^0=1[/tex]
For (1,5)
f(1) = [tex]5^1=5[/tex]
For (2,25)
f(2) = [tex]5^2=25[/tex]
For (3,125)
f(3) = [tex]5^3=125[/tex]
So all values are satisfied Option D is the correct answer.
