Answer:
1) D
2) C
3) A
4) B
Step-by-step explanation:
Ok, we need to try each function in the point x = 0 and then analyze the limit as x goes to really large values.
1) g(x) = -3^x
When x = 0, we have:
g(0) = -3^0 = -1
Then we know that the graph of this function will be either A or D.
Now, as x goes to really large values, 3^x will eventually approximate to infinity.
Then - 3^x will approximate to negative infinnity.
From that, we can conclude that the graph for this function is the one that goes to negative infinite as x increases. That is graph D.
2) h(x) = (1/3)^(-x) = 3^x
This is the exact opposite of the previous function. So we need to find the graph that is an exact reflection across the x-axis of graph D, and that one is the graph C.
then the graph if this function is C.
3) k(x) = - (1/3)^x = -1/(3^x)
When x = 0
k(0) = -(1/3)^0 = -1
We have two options with a y-intersect at y = -1 (graph A and D) and in this case, we can see that the part that grows fast is in the denominator, then as x increases, the denominator increases, and thus the function will tend to zero, then the graph of this function is graph A.
4) g(x) = 3^(-x) = 1/(3^x)
g(0) = 1/(3^0) = 1/1 = 1
And same as before, as x increases, g(x) tends to zero.
Then the remaining graph (B) is the graph of this function.
