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shtirl [24]
3 years ago
14

In Microsoft Excel, you have data that has been entered into cell A1. You need a function that looks up this value from A1 in a

table of values in E1 through F10. You need to have the value from the second column (F) be displayed in the cell in which you are writing this formula. Also, A1 will precisely match one of the values in the first column (E). What formula would you write to look up this information?
Mathematics
1 answer:
bazaltina [42]3 years ago
6 0

I'm going to assume that there is something in A1 but the way you are describing the problem, you could just as easily write a constant in the formula you are using in cells E1 to E10 and F1 to F10

The trick is to refer to A1 as $A$1 which means that E1 to E10 isn't going to get creative and start looking for things in a1 to a10.

Here is an actual table made from what I think you mean

1 113 114

2 114 116

3 115 118

4 116 120

5 117 122

6 118 124

7 119 126

8 120 128

9 121 130

10 122 132

1 to 10 on the left is in column  D

A1 contains 112

In column E the enteries from 1 to 10 simply take = $A$1 + d1

Column F uses $A$1 and adds 2*d to 112

Here is the chart shown in formula form.

1 =D1+$A$1 =$A$1 + 2*D1

2 =D2+$A$1 =$A$1 + 2*D2

3 =D3+$A$1 =$A$1 + 2*D3

4 =D4+$A$1 =$A$1 + 2*D4

5 =D5+$A$1 =$A$1 + 2*D5

6 =D6+$A$1 =$A$1 + 2*D6

7 =D7+$A$1 =$A$1 + 2*D7

8 =D8+$A$1 =$A$1 + 2*D8

9 =D9+$A$1 =$A$1 + 2*D9

10 =D10+$A$1 =$A$1 + 2*D10

Remember that 1 to 10 is in d1 to d10

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  • Domain: All the real values except x = 2 and x = 4: R - {2, 4}
  • Holes: x = 2
  • VA, vertical asymptores: x = 4
  • HA: horizontal asymptotes: there are not horizontal asymptotes
  • OA: oblique asymptotes: x + 6 [note that OH does not stand for any known feature, and so it is understood that it was intended to write OA]
  • Roots: x = 2
  • Y-intercept: -1

Step-by-step explanation:

1. <u>Given</u>:

f(x)=\frac{x^3-8}{x^2-6x+8}

  • Note that the number 8 in the numerator is not part of the power.
  • Type of function: rational function

2. <u>Domain</u>: is the set of x-values for which the function is defined.

The given function is defined for all x except those for which the denominator equals 0.

  • Denominator:  x² -6x + 8 = 0
  • Solve for x:

        Factor. (x - 4 )(x - 2) = 0

        Zero product property: (x - 4) = 0 or (x - 2) = 0

        x - 4 = 0 ⇒ x = 4

        x - 2 = 0 ⇒ x = 2

  • Domain:

        All the real values except x = 2 and x = 4: x ∈ R / x ≠ 2 and x ≠ 4.

3. <u>Holes</u>:

The holes on the graph of a rational function are at those x-values for which both the numerator and denominator are zero.

  • Find the values for which the numerator is zero:

        Numerator: x³ - 8 = 0

        Factor using difference of cubes property:

                   a³ - b³ = (a - b)(a² + ab + b²)

                   x³ - 8 = (x - 2)(x² + 2x + 4) = 0

        Zero product property:  (x - 2)(x² + 2x + 4) = 0

                    x - 2 = 0 ⇒ x = 2                    

                    x² + 2x + 4 = 0 (this has not real solution)

  • The values for which the denominator is zero were determined above: x = 2 and x = 4.

  • Conclusion: for x = 2 both numerator and denominator equal 0, so this is a hole.

4. <u>VA: Vertical asymptotes</u>.

The vertical asymptotes on the graph of a rational function are the vertical lines for which only the denominator (and not the numerator) equals zero.

  • In the previous part it was determined that happens when x = 4.

5. <u>HA: Horizontal asymptotes</u>.

In rational functions, if the numerator is a higher degree polynomial than the denominator, there is no horizontal asymptote.

6. <u>OA: oblique asymptotes</u>

  • Find the quotient and the remainder.

                       x + 6

                  _______________

x² - 6x + 8 )   x³ + 0x² + 0x - 8

                  - x³ + 6x² - 8x

                   ___________

                          6 x² -   8x -  8

                        - 6x² + 36x - 48

                        _____________

                                    28x  - 56

Result: (x + 6) + (28x - 56) / (x² - 6x + 8)

  • Find limit x → ∞

\lim_{x \to \infty}(x + 6) + \frac{28x-56}{x^2-6x+8}=x+6

<u>7. Roots</u>:

Roots are the values for which f(x) = 0.

That happens when the numerator equals 0, and the denominator is not 0.

As determined earlier: x³ - 8 = 0 ⇒ x = 2.

8. <u>Y-Intercept</u>

The y-intercepts of any function are the y-values when x = 0

  • Substitute x = 0 into the function:

         f(x)=\frac{x^3-8}{x^2-6x+8}=\frac{0^3-8}{0^2-6(0)+8}}=\frac{-8}{8} =-1

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