Answer :
To complete the sentence regarding the graph of the function [tex]\( f(z) = 16^z \)[/tex], we need to determine the values of the function at the given points [tex]\( z = -1 \)[/tex], [tex]\( z = 0 \)[/tex], and [tex]\( z = 1 \)[/tex].
1. For [tex]\( z = -1 \)[/tex]:
- Let's calculate [tex]\( f(-1) \)[/tex].
- Substitute [tex]\( z = -1 \)[/tex] into the function: [tex]\( f(-1) = 16^{-1} \)[/tex].
- This is equivalent to [tex]\( \frac{1}{16} \)[/tex] which simplifies to 0.0625.
- Therefore, [tex]\( f(-1) = 0.0625 \)[/tex].
2. For [tex]\( z = 0 \)[/tex]:
- Let's calculate [tex]\( f(0) \)[/tex].
- Substitute [tex]\( z = 0 \)[/tex] into the function: [tex]\( f(0) = 16^0 \)[/tex].
- Any number raised to the power of 0 is 1.
- Therefore, [tex]\( f(0) = 1 \)[/tex].
3. For [tex]\( z = 1 \)[/tex]:
- Let's calculate [tex]\( f(1) \)[/tex].
- Substitute [tex]\( z = 1 \)[/tex] into the function: [tex]\( f(1) = 16^1 \)[/tex].
- Any number raised to the power of 1 is the number itself.
- Therefore, [tex]\( f(1) = 16 \)[/tex].
So, the graph of [tex]\( f(z) = 16^z \)[/tex] passes through the points [tex]\( (-1, 0.0625), (0, 1), \)[/tex] and [tex]\( (1, 16) \)[/tex].
1. For [tex]\( z = -1 \)[/tex]:
- Let's calculate [tex]\( f(-1) \)[/tex].
- Substitute [tex]\( z = -1 \)[/tex] into the function: [tex]\( f(-1) = 16^{-1} \)[/tex].
- This is equivalent to [tex]\( \frac{1}{16} \)[/tex] which simplifies to 0.0625.
- Therefore, [tex]\( f(-1) = 0.0625 \)[/tex].
2. For [tex]\( z = 0 \)[/tex]:
- Let's calculate [tex]\( f(0) \)[/tex].
- Substitute [tex]\( z = 0 \)[/tex] into the function: [tex]\( f(0) = 16^0 \)[/tex].
- Any number raised to the power of 0 is 1.
- Therefore, [tex]\( f(0) = 1 \)[/tex].
3. For [tex]\( z = 1 \)[/tex]:
- Let's calculate [tex]\( f(1) \)[/tex].
- Substitute [tex]\( z = 1 \)[/tex] into the function: [tex]\( f(1) = 16^1 \)[/tex].
- Any number raised to the power of 1 is the number itself.
- Therefore, [tex]\( f(1) = 16 \)[/tex].
So, the graph of [tex]\( f(z) = 16^z \)[/tex] passes through the points [tex]\( (-1, 0.0625), (0, 1), \)[/tex] and [tex]\( (1, 16) \)[/tex].
