Questions: What function is graphed below? f(x)=-3 * e^x+2 f(x)=-2 e^x+3 f(x)=2 e^x-3 f(x)=3 e^x-3 f(x)=3 e^x-2 f(x)=-2 e^x+2

Solution Steps

The graph shows an exponential decay function, which means it is of the form \( f(x) = ae^{bx} + c \) where \( a \) is negative and \( b \) is positive.

The y-intercept occurs when \( x = 0 \). From the graph, when \( x = 0 \), \( y = 3 \).

Substitute \( x = 0 \) into the given options to see which one gives \( f(0) = 3 \):

• \( f(x) = -3e^x + 2 \) gives \( f(0) = -3e^0 + 2 = -3 + 2 = -1 \)
• \( f(x) = -2e^x + 3 \) gives \( f(0) = -2e^0 + 3 = -2 + 3 = 1 \)
• \( f(x) = 2e^x - 3 \) gives \( f(0) = 2e^0 - 3 = 2 - 3 = -1 \)
• \( f(x) = 3e^x - 3 \) gives \( f(0) = 3e^0 - 3 = 3 - 3 = 0 \)
• \( f(x) = 3e^x - 2 \) gives \( f(0) = 3e^0 - 2 = 3 - 2 = 1 \)
• \( f(x) = -2e^x + 2 \) gives \( f(0) = -2e^0 + 2 = -2 + 2 = 0 \)

None of the options give \( f(0) = 3 \). Re-evaluate the options and the graph.

Given the graph's shape and the y-intercept, the correct function should be:

• \( f(x) = -2e^x + 3 \)

Final Answer