Question
Determine if the function below is linear or exponential then fill in the guided sentences below.
xx 00 11 22 33
f, of, xf(x) minus, 3−3 minus, 1−1 11 33
Answer
Attempt 1 out of 2
The function is
because as xx increases, the yy values change
. The
of this function is exactly
.
xx 00 11 22 33
f, of, xf(x) minus, 3−3 minus, 1−1 11 33
Answer
Attempt 1 out of 2
The function is
because as xx increases, the yy values change
. The
of this function is exactly
.
Answers
GPT-4o mini
To determine whether the function is linear or exponential, we can look at how the values of \( f(x) \) change as \( x \) increases.
- When \( x = 0 \), \( f(0) = -3 \)
- When \( x = 1 \), \( f(1) = -1 \)
- When \( x = 2 \), \( f(2) = 1 \)
- When \( x = 3 \), \( f(3) = 3 \)
Now let's calculate the changes:
- From \( x = 0 \) to \( x = 1 \): \( -1 - (-3) = 2 \)
- From \( x = 1 \) to \( x = 2 \): \( 1 - (-1) = 2 \)
- From \( x = 2 \) to \( x = 3 \): \( 3 - 1 = 2 \)
The change in \( f(x) \) is constant at \( 2 \) for each unit increase in \( x \), which means the function represents a linear relationship.
Now we can fill in the guided sentences:
The function is **linear** because as \( x \) increases, the \( y \) values change **by a constant amount**. The **slope** of this function is exactly **2**.
- When \( x = 0 \), \( f(0) = -3 \)
- When \( x = 1 \), \( f(1) = -1 \)
- When \( x = 2 \), \( f(2) = 1 \)
- When \( x = 3 \), \( f(3) = 3 \)
Now let's calculate the changes:
- From \( x = 0 \) to \( x = 1 \): \( -1 - (-3) = 2 \)
- From \( x = 1 \) to \( x = 2 \): \( 1 - (-1) = 2 \)
- From \( x = 2 \) to \( x = 3 \): \( 3 - 1 = 2 \)
The change in \( f(x) \) is constant at \( 2 \) for each unit increase in \( x \), which means the function represents a linear relationship.
Now we can fill in the guided sentences:
The function is **linear** because as \( x \) increases, the \( y \) values change **by a constant amount**. The **slope** of this function is exactly **2**.