Question

Which graph models the function f(x) = −4(2)x?

exponential function going through point 0, 4 and ending up on the right
exponential function going through point 0, negative four and ending up on the right
exponential function going through point 0, negative four and ending down on the right
exponential function going through point 0, 4 and ending down on the right

Answer 1

To analyze the function \( f(x) = -4(2^x) \), we can break it down:

1. The term \( 2^x \) is an exponential function that increases as \( x \) increases. The graph of \( 2^x \) passes through the point \( (0, 1) \).

2. The function \( f(x) = -4(2^x) \) scales the \( 2^x \) graph by -4, which means:
- The graph will reflect over the x-axis because of the negative sign.
- The function scales vertically by a factor of 4. For example, at \( x = 0 \), \( f(0) = -4(2^0) = -4(1) = -4 \).

3. As \( x \) increases, \( 2^x \) increases, but since it's multiplied by -4, \( f(x) \) will decrease, approaching negative infinity.

So, the properties of the function are:
- It passes through the point \( (0, -4) \).
- It decreases as \( x \) increases.

Given these points, the correct description of the graph of the function \( f(x) = -4(2^x) \) is:

**Exponential function going through point 0, negative four and ending down on the right.**