Question

Select all the correct answers. Exponential function f is represented by the table. x 0 1 2 3 4 f(x) -12 -4 0 2 3 Function g is represented by the equation. g(x)=-12(1/3)^x Which statements are true about the two functions? Both functions are increasing on all intervals of x. The functions have the same y-intercept. Both functions approach the same value as x approaches ∞. Both functions approach -∞ as x approaches -∞. The functions have the same x-intercept.

Answer 1

Answer:

Both functions are increasing on all intervals of x: True

Both functions have the same y intercept: True

Both functions approach the same value as x approaches infinity: True

Both functions approach negative infinity as x approaches negative infinity: True.

The functions have the same x intercept: False, they have no x intercept.

Step-by-step explanation:

f(x) is stated to be an exponetial function, hence

$f(x)=ab^{x}$

f(0) is given as -12, so

-12=a

f(1) is given as -4, so

-4=-12b

b=1/3

This implies that

$f(x)=-12(\frac{1}{3})^{x}$

g(x) is stated to be

$g(x)=-12(\frac{1}{3})^{x}$

Conclusion: the functions are identical.

Answer 2

Answer:

so the answers are

the functions have the same y-intercept

both functions approach negative infinity as x approaches infinity

both functions are increasing on all intervals of x