Graphing Mid Chapter Review
Chapter
Chapter 4
Section
Graphing Mid Chapter Review
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Solutions 40 Videos

Determine where g(x) =2x^3 -3x^2 -12x + 15 is increasing and where it is decreasing.

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Q2

Graph f(x) if f'(x) < 0 when x < -2 and x >3, f'(x) > 0 when -2< x < 3, f(-2) =0, and f(3) = 5.

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Q3

Find all the critical numbers of the function.

\displaystyle y = -2x^2 + 16x - 31

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Q4a

Find all the critical numbers of the function.

\displaystyle y = x^3 -27x

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Q4b

Find all the critical numbers of the function.

\displaystyle y = x^4 -4x^2

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Q4c

Find all the critical numbers of the function.

\displaystyle y = 3x^5 -25x^3 + 60x

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Q4d

Find all the critical numbers of the function.

\displaystyle y = \frac{x^2 -1}{x^2 +1}

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Q4e

Find all the critical numbers of the function.

\displaystyle y = \frac{x}{x^2 +2}

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Q4f

Find the local max and min values.

\displaystyle g(x) = 2x^3 -9x^2 + 12x

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Q5a

Find the local max and min values.

\displaystyle g(x) =x^3 -2x^2 -4x

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Q5b

Find a value of k that gives f(x) = x^2 + kx + 2 a local minimum value of 1.

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Q6

For f(x) = x^4 -32x + 4, find the critical numbers, the intervals on which the function increases and decreases, and all the local extrema.

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Q7

Find the vertical asymptote(s) of the graph of each function. Describe the behaviour of f(x) to the left and right of each asymptote.

\displaystyle f(x) = \frac{x-1}{x+ 2}

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Q8a

Find the vertical asymptote(s) of the graph of each function. Describe the behaviour of f(x) to the left and right of each asymptote.

\displaystyle f(x) = \frac{1}{9-x^2}

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Q8b

Find the vertical asymptote(s) of the graph of each function. Describe the behaviour of f(x) to the left and right of each asymptote.

\displaystyle f(x) = \frac{x^2 -4}{3x + 9}

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Q8c

Find the vertical asymptote(s) of the graph of each function. Describe the behaviour of f(x) to the left and right of each asymptote.

\displaystyle f(x) = \frac{2-x}{3x^2 -13x -10}

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Q8d

Determine the equations of nay horizontal asymptotes. Then state whether the curve approaches the asymptote from above or below.

\displaystyle y = \frac{3x -1}{x+ 5}

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Q9a

Determine the equations of nay horizontal asymptotes. Then state whether the curve approaches the asymptote from above or below.

\displaystyle y = \frac{x^2 +3x -2}{(x -1)^2}

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Q9b

State the type of discontinuity if it exists and where. Find the limit to determine the behaviour of the curve on either side of the asymptote.

\displaystyle f(x) = \frac{x}{(x-5)^2}

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Q10a

State the type of discontinuity if it exists and where. Find the limit to determine the behaviour of the curve on either side of the asymptote.

\displaystyle f(x) = \frac{5}{x^2 + 9}

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Q10b

State the type of discontinuity if it exists and where. Find the limit to determine the behaviour of the curve on either side of the asymptote.

\displaystyle f(x) = \frac{x-2}{x^2 -12x + 12}

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Q10c

Graph y = f'(x) for the function shown below.

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Q14

Determine the equations of any vertical or horizontal asymptotes for each function. Describe the behaviour of the function on each side of any vertical or horizontal asymptote.

\displaystyle f(x) = \frac{x-5}{2x + 1}

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Q16a

Determine the equations of nay horizontal asymptotes. Then state whether the curve approaches the asymptote from above or below.

\displaystyle g(x) = \frac{x^2 -4x - 5}{(x + 2)^2}

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Q16b

Determine the equations of nay horizontal asymptotes. Then state whether the curve approaches the asymptote from above or below.

`$\displaystyle g(x) = \frac{x^2 + 2x -15}{9-x^2} $

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Q16c

Determine the equations of nay horizontal asymptotes. Then state whether the curve approaches the asymptote from above or below.

`$\displaystyle g(x) = \frac{2x^2 + x + 1}{x + 4} $

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Q16d

Find the limit.

\displaystyle \lim_{x\to \infty} \frac{3-2x}{3x}

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Q17a

Find the limit.

\displaystyle \lim_{x\to \infty} \frac{x^2 -2x + 5}{6x^2 +2x -1}

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Q17b

Find the limit.

\displaystyle \lim_{x\to \infty} \frac{7 + 2x^2 -3x^3}{x^3 -4x^2 + 3x}

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Q17c

Find the limit.

\displaystyle \lim_{x\to \infty} \frac{5-2x^3}{x^4 -4x}

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Q17d

Find the limit.

\displaystyle \lim_{x\to \infty} \frac{2x^5 -1}{3x^4 -x^2 -2}

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Q17e

Find the limit.

\displaystyle \lim_{x\to \infty} \frac{x^2 + 3x - 18}{(x-3)^2}

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Q17f

Find the limit.

\displaystyle \lim_{x\to \infty} \frac{x^2 -4x - 5}{x^2 -1}

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Q17g

Find the limit.

\displaystyle \lim_{x\to \infty} (5x + 4 - \frac{7}{x + 3})

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Q17h