Answer: B: 0 < a < 1
Step-by-step explanation:
The equation we have is:
f(x) = a^(x + h) + k.
k is the value at where we have the horizontal line. In this particular case, we can see that we have a horizontal line at y = -4, then we can conclude that:
k ≈ -4
a is the rate of growth. If a is positive and greater than 1, we would have an increasing function, for example with a = 2, k = 0 and h = 0 we have:
2^1 = 2
2^2 =4
2^3 = 8
This is an increasing function.
Now if a is greater than 0 and smaller than 1, we have a decreasing function (as seen in the graph). For example for a = 0.5, k = 0 and h = 0 we have:
0.5^1 = 0.5
0.5^2 = 0.25
0.5^3 = 0.125
This is a decreasing function.
Then the correct option is B, 0 < a < 1
