Find the $ y $ intercept of $ f(x)= \frac{4x^2+3}{6x+3} +-7 $Give your answer correct to 2 decimal places.

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BlackTom AI · Accepted Answer

The question asks for the y-intercept of f(x) = (4x^2 + 3)/(6x + 3) ± 7, with the value given to 2 decimal places.

To find the y-intercept, we evaluate the function at x = 0, since the y-intercept is the point where the graph crosses the y-axis (x = 0).

First, compute the rational part at x = 0: (4(0)^2 + 3) / (6(0) + 3) = 3 / 3 = 1.

Now apply the ± 7 from the expression. There are two possible interpretations due to the ± sign:
- If the expression uses +7, the y-intercept is 1 + 7 = 8.
- If the expression uses −7, the y-intercept is 1 − 7 = −6.

Thus, depending on whether the plus or minus is chosen, the y-intercept could be 8 or −6. Since the prompt asks for a numerical value and the answer shown is −6, that corresponds to the case where the expression involves subtracting 7 (i.e., the −7 branch).

If you were to present the result to two decimal places, −6 would be written as −6.00. In summary:
- Case with +7: y-intercept = 8 → 8.00 when rounded to two decimals.
- Case with −7: y-intercept = −6 → −6.00 when rounded to two decimals.

The final value selected in the provided answer is −6.00, which matches the −7 branch of the ±7 term.

UCIC 202503 EMTH118 Quiz 9

Find the \( y \) intercept of \( f(x)= \frac{4x^2+3}{6x+3} +-7 \)Give your answer correct to 2 decimal places.

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