Question

Which graph represents the function of f(x) = 4x² - 4x -8/2x+2.​

Answer 1

I think that second option represents the function of f(x) = 4x² - 4x -8/2x+2.

Answer 2

The lower graph seems to fit this description, as the line appears to have a positive slope and intersects the y-axis around -4.

The function provided is
`\( f(x) = (4x^2 - 4x - 8)/(2x + 2) \)`. To simplify this function, we can factor out common terms in the numerator and the denominator.

Let's break down the simplification process:

1. Factor the numerator
`\( 4x^2 - 4x - 8 \):`

We can factor out a 4 from each term:
`\( 4(x^2 - x - 2) \).`

Next, we factor the quadratic:
`\( 4((x - 2)(x + 1)) \).`

2. Factor the denominator
`\( 2x + 2 \):`

We can factor out a 2:
`\( 2(x + 1) \).`

3. Now, the function looks like
`\( f(x) = (4(x - 2)(x + 1))/(2(x + 1)) \).`

4. We can cancel out the
`\( (x + 1) \)` terms:

`\[ f(x) = (4(x - 2))/(2) \]`

5. This simplifies further to:

`\[ f(x) = 2(x - 2) \]`

6. Finally, we have:

`\[ f(x) = 2x - 4 \]`

This is a linear function with a slope of 2 and a y-intercept of -4. The graph of a linear function is a straight line. Between the two graphs provided, we're looking for the graph that shows a straight line with a positive slope (since our slope is 2) and crosses the y-axis at -4.

To identify the correct graph among the two, we should:

- Check which graph has a y-intercept at -4.

- Check that the slope of the line is positive (rises as it moves from left to right).

The lower graph seems to fit this description, as the line appears to have a positive slope and intersects the y-axis around -4.

If this matches one of the graphs shown in the image, that graph represents the function
`\( f(x) = 4x^2 - 4x - 8/2x+2 \)` after simplification. If more precise identification is needed, we would have to use exact points on the graph to confirm the slope and y-intercept.