Answer:
The correct options are 1 and 3.
Step-by-step explanation:
The given function is
[tex]g(x)=20(1.5)^x[/tex]
1.
From the given table the value of f(x) is -33 at x=1, so
[tex]f(1)=-33[/tex]
Substitute x=-1 in g(x), to find the value of g(-1).
[tex]g(-1)=20(1.5)^{-1}=13.33[/tex]
Since -33<13.33, therefore f(1) is less than g(−1) and statement 1 correct.
2.
From the table it is notices that the value of f(x) is -45 at x=-5 and -49 at x=-3.
The rate of change is
[tex]m=\frac{-49-(-45)}{-3-(-5)}=\frac{-4}{2}=-2[/tex]
The function g(x) is a growth function because the exponent 1.5>1, therefore the rate of change is always positive.
So, the rate of change of g(x) is greater than the f(x).
The statement "f(x) increases at a faster rate than g(x) does on the interval (−5, −3)" is incorrect.
3.
From the given table it is notices that the y-intercept is -40 because the function intersects the y-axis at (0,-40).
Substitute x=0 in g(x).
[tex]g(0)=20(1.5)^0=20[/tex]
Since g(x) has a greater y-intercept than f(x) does, therefore statement 3 is correct.
4.
From the given table it is noticed that the function f(x) first decreases and after that it increases on the interval [tex](-\infty, \infty)[/tex].
The function g(x) is a growth function, therefore the function g(x) increases on the interval [tex](-\infty, \infty)[/tex].
Since the function f(x) is not satirically increasing on the interval [tex](-\infty, \infty)[/tex], therefore statement 4 is incorrect.
