To compare the exponential functions given, let's first understand their respective behaviors:
### Function 1: [tex]\( y = 4^x \)[/tex]
- This is a typical exponential growth function because the base [tex]\( 4 \)[/tex] is greater than [tex]\( 1 \)[/tex].
- Exponential growth functions generally have an L-shaped curve that increases rapidly as [tex]\( x \)[/tex] increases. For large values of [tex]\( x \)[/tex], [tex]\( y \)[/tex] increases very quickly.
- For negative [tex]\( x \)[/tex] values, [tex]\( y \)[/tex] approaches [tex]\( 0 \)[/tex] but never actually reaches it, thus forming the L-shaped curve.
### Function 2: A function is increasing exponentially and passes through the point [tex]\( (0, 1) \)[/tex]
- An exponential function that passes through the point [tex]\( (0, 1) \)[/tex] can be written as [tex]\( y = b^x \)[/tex] where [tex]\( b \)[/tex] is any positive number greater than [tex]\( 1 \)[/tex].
- Like Function 1, this function will also exhibit exponential growth and will have an L-shaped curve as described above.
Given the descriptions of both functions:
- Both functions exhibit exponential growth and thus have similar L-shaped curves.
- It is not accurate to say either of these functions has a reversed L-shaped curve because in exponential growth, the curves are always increasing and never decrease as [tex]\( x \)[/tex] increases.
With these observations, the most accurate statement comparing Function 1 and Function 2 is:
“Function 1 has an L-shaped curve, and Function 2 has a reversed ∠-shaped curve.”
Therefore, the correct statement is:
Function 1 has an L-shaped curve, and Function 2 has a reversed ∠-shaped curve.
