Question
se the table to answer the question.
x y
0 3
1 3 1/4
2 4
3 4 1/2
Export to Sheets
Which of the following equations describes the function in the table using function notation?
Answer Options:
f(x) = 1/4x + 3
f(x) = 3x + 1/4
f(x) = 1/2x + 3
f(x) = 1/2x + 3
x y
0 3
1 3 1/4
2 4
3 4 1/2
Export to Sheets
Which of the following equations describes the function in the table using function notation?
Answer Options:
f(x) = 1/4x + 3
f(x) = 3x + 1/4
f(x) = 1/2x + 3
f(x) = 1/2x + 3
Answers
Answered by
GPT-4o mini
To determine which equation describes the function in the table, we need to analyze the provided data points and identify a pattern.
The points given in the table are:
- (0, 3)
- (1, 3 1/4) = (1, 3.25)
- (2, 4)
- (3, 4 1/2) = (3, 4.5)
Now, let's examine how the value of \( y \) changes as \( x \) increases:
1. From \( x = 0 \) to \( x = 1 \):
- \( y \) changes from 3 to 3.25 (which is an increase of 0.25).
2. From \( x = 1 \) to \( x = 2 \):
- \( y \) changes from 3.25 to 4 (an increase of 0.75).
3. From \( x = 2 \) to \( x = 3 \):
- \( y \) changes from 4 to 4.5 (an increase of 0.5).
For each increase of \( x \) by 1, \( y \) doesn't increase uniformly. Thus, it seems to be a piecewise function or a function that doesn't fit into a linear equation straightforwardly.
Next, let's evaluate the equations provided:
1. \( f(x) = \frac{1}{4}x + 3 \)
- When \( x = 0, f(0) = 3\)
- When \( x = 1, f(1) = \frac{1}{4}(1) + 3 = 3.25 \)
- When \( x = 2, f(2) = \frac{1}{4}(2) + 3 = 3.5 \)
- When \( x = 3, f(3) = \frac{1}{4}(3) + 3 = 3.75\)
This does not match \( y \)-values.
2. \( f(x) = 3x + \frac{1}{4} \)
- When \( x = 0, f(0) = 0 \times 3 + 0.25 = 0.25\)
- Not matching.
3. \( f(x) = \frac{1}{2}x + 3 \)
- When \( x = 0, f(0) = 3\)
- When \( x = 1, f(1) = \frac{1}{2}(1) + 3 = 3.5\)
- Does not match fully.
Since none of the options fit the derived values correctly, it is possible there's a miscalculation or misunderstanding of those function characteristics. However, based on what we observed, the best-fitting equation looks to be the first one:
**Answer:** \( f(x) = \frac{1}{4}x + 3 \)
Please double-check your function assumptions; if there are further details regarding calculations or function types, those could help refine which is most suitable.
The points given in the table are:
- (0, 3)
- (1, 3 1/4) = (1, 3.25)
- (2, 4)
- (3, 4 1/2) = (3, 4.5)
Now, let's examine how the value of \( y \) changes as \( x \) increases:
1. From \( x = 0 \) to \( x = 1 \):
- \( y \) changes from 3 to 3.25 (which is an increase of 0.25).
2. From \( x = 1 \) to \( x = 2 \):
- \( y \) changes from 3.25 to 4 (an increase of 0.75).
3. From \( x = 2 \) to \( x = 3 \):
- \( y \) changes from 4 to 4.5 (an increase of 0.5).
For each increase of \( x \) by 1, \( y \) doesn't increase uniformly. Thus, it seems to be a piecewise function or a function that doesn't fit into a linear equation straightforwardly.
Next, let's evaluate the equations provided:
1. \( f(x) = \frac{1}{4}x + 3 \)
- When \( x = 0, f(0) = 3\)
- When \( x = 1, f(1) = \frac{1}{4}(1) + 3 = 3.25 \)
- When \( x = 2, f(2) = \frac{1}{4}(2) + 3 = 3.5 \)
- When \( x = 3, f(3) = \frac{1}{4}(3) + 3 = 3.75\)
This does not match \( y \)-values.
2. \( f(x) = 3x + \frac{1}{4} \)
- When \( x = 0, f(0) = 0 \times 3 + 0.25 = 0.25\)
- Not matching.
3. \( f(x) = \frac{1}{2}x + 3 \)
- When \( x = 0, f(0) = 3\)
- When \( x = 1, f(1) = \frac{1}{2}(1) + 3 = 3.5\)
- Does not match fully.
Since none of the options fit the derived values correctly, it is possible there's a miscalculation or misunderstanding of those function characteristics. However, based on what we observed, the best-fitting equation looks to be the first one:
**Answer:** \( f(x) = \frac{1}{4}x + 3 \)
Please double-check your function assumptions; if there are further details regarding calculations or function types, those could help refine which is most suitable.
There are no human answers yet. A form for humans to post answers is coming very soon!