# Explanation: ## Step1: Analyze the function type The function $ y = - (4)^x $ is an exponential function. The base $ 4>1 $, so the parent function $ y = 4^x $ is an increasing exponential function. The negative sign reflects it over the $ x $-axis. ## Step2: Check key points - When $ x = 0 $, $ y=-4^0=- 1 $. So the graph passes through $ (0, - 1) $. - As $ x\to+\infty $, $ 4^x\to+\infty $, so $ y=-4^x\to-\infty $. - As $ x\to-\infty $, $ 4^x\to0 $, so $ y = - 4^x\to0 $. Now check the graphs: - The first graph is increasing (for $ y = 4^x $ type), but our function is decreasing after reflection, so eliminate. - The second graph is a parabola - like (even function), but our function is not even (since $ f(-x)=-4^{-x} eq f(x) $), so eliminate. - The third graph: passes through $ (0, - 1) $, as $ x$ increases, $ y$ decreases to $ -\infty $, as $ x$ decreases, $ y$ approaches $ 0 $, which matches our function. # Answer: The third graph (the one at the bottom)

graph $y = -(4)^x$.

QUESTION IMAGE

Question

graph $y = -(4)^x$.

Explanation:

Step1: Analyze the function type

The function $ y = - (4)^x $ is an exponential function. The base $ 4>1 $, so the parent function $ y = 4^x $ is an increasing exponential function. The negative sign reflects it over the $ x $-axis.

Step2: Check key points

When $ x = 0 $, $ y=-4^0=- 1 $. So the graph passes through $ (0, - 1) $.
As $ x\to+\infty $, $ 4^x\to+\infty $, so $ y=-4^x\to-\infty $.
As $ x\to-\infty $, $ 4^x\to0 $, so $ y = - 4^x\to0 $.

Now check the graphs:

The first graph is increasing (for $ y = 4^x $ type), but our function is decreasing after reflection, so eliminate.
The second graph is a parabola - like (even function), but our function is not even (since \( f(-x)=-4^{-x}

eq f(x) \)), so eliminate.

The third graph: passes through $ (0, - 1) $, as $ x$ increases, $ y$ decreases to $ -\infty $, as $ x$ decreases, $ y$ approaches $ 0 $, which matches our function.

Answer:

The third graph (the one at the bottom)