You have two exponential functions. one has the formula h(x) = 3^x – 2. the other function, g(x), has the graph shown below. which inequality below is true for all points on the indicated interval? g(x) ≥ h(x) on the interval –2 ≤ x ≤ 2 g(x) ≥ h(x) on the interval –3 ≤ x ≤ 3 g(x) ≤ h(x) on the interval –3 ≤ x ≤ 3 g(x) ≤ h(x) on the interval –2 ≤ x ≤ 2

h(x) = 3^x – 2 will be negative  when x is less than 0

h(2) =7

g(2)=7

This is the point they are equal

g(x)> h(x) until2

g(x)>=h(x) -2<=x<=2

Choice A

Option A.

Step-by-step explanation:

The given function is

       ... (1)

It is an exponential function.

The graph of second exponential function passes through the points (0,4) and (1,5), and it shifted 3 units up.

Substitute x=0 and g(x)=4 in the above function.

Substitute a=1, x=1 and g(x)=5 in the above function.

The second function is

            .... (2)

At x=0,

So, at initial stage g(x)>h(x).

On solving (1) and (2) we get

It means at x=2 the function h(x) is equal to g(x) and after that h(x)>g(x).

g(x) ≥ h(x) on the interval –2 ≤ x ≤ 2

Therefore, the correct option is A.

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.