7. Evaluate the function below over the domain {-1, 0,
1, 2}. As the values of the domain increase, do the
values of the function increase or decrease?
y = (3/4)ˣ
Decrease.
To evaluate the function y = (3/4)^x over the domain {-1, 0, 1, 2}, we substitute each value from the domain into the function and find the corresponding y-values.
1. For x = -1:
y = (3/4)^(-1) = 4/3 ≈ 1.333
2. For x = 0:
y = (3/4)^0 = 1
3. For x = 1:
y = (3/4)^1 = 3/4 = 0.75
4. For x = 2:
y = (3/4)^2 = 9/16 ≈ 0.563
As we increase the values of the domain from -1 to 2, we see that the values of the function decrease.
To evaluate the function y = (3/4)ˣ over the domain {-1, 0, 1, 2}, we can substitute each value of the domain into the function and solve for y.
Let's go step by step:
1. Substitute -1 into the function:
y = (3/4)^(-1)
Now, we need to evaluate (3/4)^(-1). To do this, we need to remember the rule that any number raised to the power of -1 is equal to its reciprocal.
(3/4)^(-1) = 4/3
So, for x = -1, y = 4/3.
2. Substitute 0 into the function:
y = (3/4)^0
Any number raised to the power of 0 is always 1.
So, for x = 0, y = 1.
3. Substitute 1 into the function:
y = (3/4)^1
Any number raised to the power of 1 remains the same.
So, for x = 1, y = 3/4.
4. Substitute 2 into the function:
y = (3/4)^2
To evaluate (3/4)^2, we need to multiply 3/4 by itself.
(3/4)^2 = (3/4) * (3/4) = 9/16
So, for x = 2, y = 9/16.
Now, let's analyze the values of the function as the values of the domain increase:
- For x = -1, y = 4/3
- For x = 0, y = 1
- For x = 1, y = 3/4
- For x = 2, y = 9/16
In this case, as the values of the domain increase from -1 to 2, the values of the function, y, decrease.