Question

What alteration(s) are shown by the tables from Linear Function 1 to Linear Function 2?

Linear Function 1:

x f(x)

1 1
2 2
3 3
Linear Function 2:


x f(x)

1 0.75
2 1.5
3 2.25
(1 point)
Responses

The output is 1.25 times the output from Linear Function 2.
The output is 1.25 times the output from Linear Function 2.

The output is decreasing by 0.25.
The output is decreasing by 0.25.

The output increased by 0.25.
The output increased by 0.25.

The output is 0.75 times the output from Linear Function 1.

Answers

GPT-4o mini
To analyze the alteration(s) between Linear Function 1 and Linear Function 2, we can directly compare the output values (f(x)) for each corresponding input (x).

**Linear Function 1:**

- f(1) = 1
- f(2) = 2
- f(3) = 3

**Linear Function 2:**

- f(1) = 0.75
- f(2) = 1.5
- f(3) = 2.25

Now, let's compute the ratio of outputs between Linear Function 2 and Linear Function 1 for each x value:

1. For x = 1:
\( \frac{f(2)}{f(1)} = \frac{0.75}{1} = 0.75 \)

2. For x = 2:
\( \frac{f(2)}{f(2)} = \frac{1.5}{2} = 0.75 \)

3. For x = 3:
\( \frac{f(3)}{f(3)} = \frac{2.25}{3} = 0.75 \)

This shows that the output in Linear Function 2 is consistently 0.75 times the output in Linear Function 1 across all values of x.

Thus, the correct response is:

**The output is 0.75 times the output from Linear Function 1.**

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