Answer:
The 4th graph (lower right)
Step-by-step explanation:
Let's quickly look at y=(1/2)*4^x and decide its basic shape. Pick a few values of x that result in an easy calculation.
x y
-1 0.125
0 0.5
1 2
2 8
3 32
We can see that the resulting graph:
1) y never goes below 0, regardless of how negative x becomes (as x decreases, the term 4^x decreases since negative x creates an inverse of 4: E.G.: 4^(-1) = (1/4), 4^-2 = (1/16), etc.),
2) has a y-intercept at 0.5, and
3) escalates exponentially upwards as x gets larger.
The graph on the lower right has a y-intercept of 0.5, never goes below y=0, and escalates rapidly with increasing x.
The other three graphs violate at least one of the properties noted above by our quick assessment of the function. Labeling the graphs 1 through 4:
1 2
3 4
Graph Violates Observation
1 2 and 3
2 1, 2 and 3 [Defined as Total Loser]
3 2
4 None. It meets all criteria.
