Question
Determine if the function below is linear or exponential then fill in the guided sentences below.
xx 22 33 44 55
f, of, xf(x) minus, 37−37 minus, 42−42 minus, 47−47 minus, 52−52
Answer
The function is
because as xx increases, the yy values change
. The
of this function is exactly
.
xx 22 33 44 55
f, of, xf(x) minus, 37−37 minus, 42−42 minus, 47−47 minus, 52−52
Answer
The function is
because as xx increases, the yy values change
. The
of this function is exactly
.
Answers
GPT-4o mini
To determine if the function is linear or exponential based on the provided data:
Given the values in the structure:
- \(x\): 2, 3, 4, 5
- Corresponding \(f(x)\) values (likely from the structure): 37, 42, 47, 52
Let's calculate the differences in \(f(x)\):
1. \(f(3) - f(2) = 42 - 37 = 5\)
2. \(f(4) - f(3) = 47 - 42 = 5\)
3. \(f(5) - f(4) = 52 - 47 = 5\)
Since the differences in the \(f(x)\) values are constant (5), this indicates that the function is linear.
Now we can fill in the guided sentences:
The function is **linear** because as \(x\) increases, the \(y\) values change **by a constant amount (5)**. The **slope** of this function is exactly **5**.
Given the values in the structure:
- \(x\): 2, 3, 4, 5
- Corresponding \(f(x)\) values (likely from the structure): 37, 42, 47, 52
Let's calculate the differences in \(f(x)\):
1. \(f(3) - f(2) = 42 - 37 = 5\)
2. \(f(4) - f(3) = 47 - 42 = 5\)
3. \(f(5) - f(4) = 52 - 47 = 5\)
Since the differences in the \(f(x)\) values are constant (5), this indicates that the function is linear.
Now we can fill in the guided sentences:
The function is **linear** because as \(x\) increases, the \(y\) values change **by a constant amount (5)**. The **slope** of this function is exactly **5**.