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

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

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.

Q3

Find all the critical numbers of the function.

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

Q4a

Find all the critical numbers of the function.

\displaystyle y = x^3 -27x 

Q4b

Find all the critical numbers of the function.

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

Q4c

Find all the critical numbers of the function.

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

Q4d

Find all the critical numbers of the function.

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

Q4e

Find all the critical numbers of the function.

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

Q4f

Find the local max and min values.

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

Q5a

Find the local max and min values.

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

Q5b

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

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.

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} 

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} 

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} 

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} 

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} 

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} 

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} 

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} 

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} 

Q10c

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

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} 

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} 

Q16b

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

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

Q16c

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

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

Q16d

Find the limit.

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

Q17a

Find the limit.

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

Q17b

Find the limit.

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

Q17c

Find the limit.

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

Q17d

Find the limit.

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

Q17e

Find the limit.

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

Q17f

Find the limit.

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

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