Sovi AI

題目

解題步驟

1. Understand the question

   fill in each blank give the following information:
   given the table below, write a possible equation for the function. 3 points
   | x | -100 | -50 | -10 | -6 | -5 | -4 | -3 | 5 | 50 | 100 |
   | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
   | y | 3.21 | 3.44 | 7 | 23 | error | -17 | -7 | 1 | 2.63 | 2.81 |
   write an equation for a rational function which has a v.a at $x=4$ and a h.a at $y=0$. 2 points
   a) ______
   b) ______

2. Explanation

   Step1: Identify vertical asymptote

   From the table, there is an error at $x=-5$, so the denominator has a factor of $(x+5)$.

   Step2: Identify horizontal asymptote

   As $x\to\pm\infty$, $y$ approaches 3. So the degrees of numerator and denominator are equal, and the leading coefficient ratio is 3. Let the function be $y=3+\frac{k}{x+5}$.

   Step3: Solve for k using a point

   Use $x=-4, y=-17$:
   $-17=3+\frac{k}{-4+5}$
   $-17=3+k$
   $k=-20$

   Step4: Verify with another point

   Check $x=-6, y=23$:
   $y=3+\frac{-20}{-6+5}=3+20=23$, which matches.

   Step5: Write equation for VA/HA

   For vertical asymptote $x=4$ and horizontal asymptote $y=0$, the rational function has denominator $(x-4)$ and numerator of lower degree. A simple form is $y=\frac{a}{x-4}$ (any non-zero $a$ works, e.g., $a=1$).

3. Final answer

   a) $y=3-\frac{20}{x+5}$
   b) $y=\frac{1}{x-4}$ (any non-zero numerator constant is valid)

答案

Question Analysis

OCR Text

fill in each blank give the following information:
given the table below, write a possible equation for the function. 3 points
| x | -100 | -50 | -10 | -6 | -5 | -4 | -3 | 5 | 50 | 100 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| y | 3.21 | 3.44 | 7 | 23 | error | -17 | -7 | 1 | 2.63 | 2.81 |
write an equation for a rational function which has a v.a at $x=4$ and a h.a at $y=0$. 2 points
a) ______
b) ______

相關知識點

關聯題目

• use an area model to solve 31 × 26. multiply in the area model.

  Top-left cell: 180 Top-right cell: 6 Bottom-left cell: 600 Bottom-right cell: 20 Final product: 806

• 6. solve each equation. write each solution as a fraction and as a deci…

  | Equation | Solution (Fraction) | Solution (Decimal) | |----------|---------------------|--------------------| | $2x=3$ | $\frac{3}{2}$ | $1.5$ | | $5y=3$ | $\frac{3}{5}$ | $0.6$…

• Ok

  - Fila 2: Circular el par (5, 2). - Fila 3: Circular el par (3, 3) (o la tarjeta con 3 y la otra con 4 dibujos, pero los números son 3 y 3? Wait, la tercera fila: primera tarjeta …

• How do you solve pemdas

  It's basically just a checklist so you don't get mixed up when a math problem has a bunch of stuff going on at once. You just go down the list in order: 1. **P**arentheses: Do any…

• which number line models $-1 + (-14)$? add. $-1 + (-14) = \\square$

  \(-15\)

• 11 et 12

  The initial number of bacteria is 5. ### Turn 2 Answer Ça marche, regardons ça ! On dirait que tu es en plein dans les maths financières. Pour le **numéro 11**, on cherche le taux…

• which of the following are polynomial functions?

  The second graph (smooth, rising/falling curve with a local max and min) and the third graph (downward-opening parabola) are polynomial functions.

• use the graph of the polynomial function shown below to identify the ze…

  | Zeros | Mult. | |-------|-------| | $-4$ | $3$ | | $0$ | $1$ | | $4$ | $2$ | | | |

Sovi AI iOS

官網：mysovi.ai。題庫頁面網域：question-banks.mysovi.ai。iOS 應用透過 Apple App Store 提供。