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Wittaler [7]
3 years ago
12

Use the graph below for this question:

Mathematics
2 answers:
Gala2k [10]3 years ago
5 0
What they want here is the slope of the line through (1,7) and (-3,9)

Using the slope formula, we get...

m = (y2-y1)/(x2-x1)
m = (9-7)/(-3-(-1))
<span>m = (9-7)/(-3+1)</span>
m = 2/(-2)
m = -1

So the answer must be choice D) -1

If you draw a line through these two points, the line will slope downward (move from left to right). Each time you go down 1, you go to the right 1. 
kirill [66]3 years ago
5 0

Answer:

The correct option is 4. The average rate of change from x = −1 to x = −3 is -1.

Step-by-step explanation:

It is given that the graph of parabola going through (-1,7) and (-3,9).

It means the value of at x=-1 is 7.

f(-1)=7

The value of at x=-3 is 9.

f(-3)=9

The slope of a function f(x) for the interval [a,b] is

m=\frac{f(b)-f(a)}{b-a}

We have to find the average rate of change from x = −1 to x = −3. Here a=-1 and b=-3. So the average rate of change from x = −1 to x = −3 is

m=\frac{f(-3)-f(-1)}{-3-(-1)}

m=\frac{9-7}{-3+1}

m=\frac{2}{-2}

m=-1

The average rate of change from x = −1 to x = −3 is -1. Therefore the correct option is 4.

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Firlakuza [10]

Answer:

  • 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

3 0
3 years ago
The graph shows the amount of money Tanya earns from tutoring compared with the number of hours she works. Select the correct st
salantis [7]

Answer:

B

Step-by-step explanation:

The graph (although it doesn't show it) is making points at every 20 (dollars) mark and also lines up to each hour mark, meaning that for every hour, Tanya makes 20 dollars.

7 0
3 years ago
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Tax is paid on meals in a restaurant.
liberstina [14]

Answer:

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Step-by-step explanation:

65.35/11.45 = 0.1752

.1752 * 100

= 17.52

4 0
2 years ago
On average, Debbie can finish 4 algebra problem in 30 minutes. If Debbie works at this rate, how many problems will she solve in
alexandr402 [8]
She will solve 20 problems in 2.5 hours, 4*5 thirty minute sessions=20.
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bagirrra123 [75]

Answer:

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i hope this helps :)

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