Question

y = -2^x
identify the graph of the function y = -2^x
a. graph
b. graph
c. graph
d. graph

Explanation:

Step1: Analyze the function \( y = -2^x \)

The parent function is \( y = 2^x \), which is an exponential growth function (increasing, passes through (0,1), and has a horizontal asymptote at \( y = 0 \) as \( x \to -\infty \)). When we multiply by -1, we reflect the graph over the x - axis. So for \( y=-2^x \):

• When \( x = 0 \), \( y=-2^0=-1\).
• As \( x\to+\infty \), \( 2^x\to+\infty \), so \( y = - 2^x\to-\infty \).
• As \( x\to-\infty \), \( 2^x\to0 \), so \( y=-2^x\to0 \) (horizontal asymptote \( y = 0 \) as \( x\to-\infty \)).

Step2: Analyze each option

• Option A: The graph is increasing, which is like \( y = 2^x \) (not reflected), so A is wrong.
• Option B: The graph is increasing and passes through (0,0) - (0,1) range? No, and it's increasing, not matching \( y=-2^x \), so B is wrong.
• Option C: Let's check the key points. When \( x = 0 \), \( y=-1 \). As \( x\to+\infty \), \( y\to-\infty \), and as \( x\to-\infty \), \( y\to0 \). The graph is decreasing (since as x increases, y decreases), which matches the behavior of \( y=-2^x \).
• Option D: The graph seems to have a horizontal asymptote as \( x\to+\infty \) approaching 0, but when \( x = 0 \), let's see the y - value. If we assume the shape, it's more like a reflection of \( y = 2^{-x}\) or something else, not \( y=-2^x \). So D is wrong.

Answer:

C