Question
2. Which of the following equations describes the function in the table using function notation?
x y
0 3
1 3 1/2
2 4
3 4 1/2
(1 point)
Responses
f(x) =3x +12
f(x) =3x +12
f(y ) =3x +12
f(y ) =3x +12
f(x ) =12x +3
f(x ) =12x +3
f(y) =12x +3
x y
0 3
1 3 1/2
2 4
3 4 1/2
(1 point)
Responses
f(x) =3x +12
f(x) =3x +12
f(y ) =3x +12
f(y ) =3x +12
f(x ) =12x +3
f(x ) =12x +3
f(y) =12x +3
Answers
Answered by
GPT-4o mini
To determine which function describes the values in the table using function notation, we can analyze the points provided.
The points given are:
- \( (0, 3) \)
- \( (1, 3.5) \)
- \( (2, 4) \)
- \( (3, 4.5) \)
If we observe the \( y \)-values:
- At \( x = 0 \), \( y = 3 \)
- At \( x = 1 \), \( y = 3.5 \)
- At \( x = 2 \), \( y = 4 \)
- At \( x = 3 \), \( y = 4.5 \)
The pattern shows that as \( x \) increases by 1, \( y \) increases by 0.5. This suggests a linear relationship.
To find the equation, we can use the slope-intercept form, \( y = mx + b \), where \( m \) is the slope, and \( b \) is the y-intercept.
1. Calculate the slope \( m \):
\[
m = \frac{\Delta y}{\Delta x} = \frac{4.5 - 3}{3 - 0} = \frac{1.5}{3} = 0.5
\]
2. Using the point \( (0, 3) \) to find \( b \):
\[
y = mx + b \implies 3 = 0.5(0) + b \implies b = 3
\]
Thus, the function is:
\[
y = 0.5x + 3
\]
To express this in function notation, we write:
\[
f(x) = 0.5x + 3
\]
Now let's see which of the options provided closely matches this function.
None of the options given appear to represent the correct linear function derived from the data in the table, so it seems there might be an error in the options provided as none represent our calculation \( f(x) = 0.5x + 3 \).
The options you've provided seem incorrect with respect to the values in the table. It would be ideal to double-check for any errors or omissions in the options listed.
The points given are:
- \( (0, 3) \)
- \( (1, 3.5) \)
- \( (2, 4) \)
- \( (3, 4.5) \)
If we observe the \( y \)-values:
- At \( x = 0 \), \( y = 3 \)
- At \( x = 1 \), \( y = 3.5 \)
- At \( x = 2 \), \( y = 4 \)
- At \( x = 3 \), \( y = 4.5 \)
The pattern shows that as \( x \) increases by 1, \( y \) increases by 0.5. This suggests a linear relationship.
To find the equation, we can use the slope-intercept form, \( y = mx + b \), where \( m \) is the slope, and \( b \) is the y-intercept.
1. Calculate the slope \( m \):
\[
m = \frac{\Delta y}{\Delta x} = \frac{4.5 - 3}{3 - 0} = \frac{1.5}{3} = 0.5
\]
2. Using the point \( (0, 3) \) to find \( b \):
\[
y = mx + b \implies 3 = 0.5(0) + b \implies b = 3
\]
Thus, the function is:
\[
y = 0.5x + 3
\]
To express this in function notation, we write:
\[
f(x) = 0.5x + 3
\]
Now let's see which of the options provided closely matches this function.
None of the options given appear to represent the correct linear function derived from the data in the table, so it seems there might be an error in the options provided as none represent our calculation \( f(x) = 0.5x + 3 \).
The options you've provided seem incorrect with respect to the values in the table. It would be ideal to double-check for any errors or omissions in the options listed.