Determine equations for the vertical and horizontal asymptotes of each function.
\displaystyle
f(x) = \frac{1}{x-2}
Determine equations for the vertical and horizontal asymptotes of each function.
\displaystyle
f(x) = \frac{3}{x+7}
Determine equations for the vertical and horizontal asymptotes of each function.
\displaystyle
f(x) = -\frac{4}{x-7}
Determine an equation to represent each function.
Determine an equation to represent each function.
Sketch a graph of each function. State the domain, range, y-intercepts, and equations of the asymptotes.
\displaystyle
f(x) = \frac{5}{x-3}
Sketch a graph of each function. State the domain, range, y-intercepts, and equations of the asymptotes.
\displaystyle
g(x) = -\frac{1}{x-4}
Sketch a graph of each function. State the domain, range, y-intercepts, and equations of the asymptotes.
\displaystyle
h(x) = \frac{1}{2x-3}
Sketch a graph of each function. State the domain, range, y-intercepts, and equations of the asymptotes.
\displaystyle
h(x) = - \frac{8}{5x+4}
Determine equations for the vertical asymptotes of the function. Then, state the domain.
\displaystyle
f(x) = \frac{1}{(x -3)(x+ 4)}
Determine equations for the vertical asymptotes of the function. Then, state the domain.
\displaystyle
f(x) = -\frac{2}{(x+ 3)^2}
Determine equations for the vertical asymptotes of the function. Then, state the domain.
\displaystyle
f(x) = \frac{1}{x^2 + 8x + 12}
,For each function,
\displaystyle
f(x) = \frac{1}{x^2 + 6x + 5}
,For each function,
\displaystyle
f(x) = \frac{1}{x^2 - 5x-24}
,For each function,
\displaystyle
f(x) = -\frac{1}{x^2 -6x + 9}
,For each function,
\displaystyle
f(x) = -\frac{2}{x^2+ 5}
Analyse the slope, and change in slope, for the
intervals of the function \displaystyle
f(x) = \frac{1}{2x^2 +3x - 5}
by sketching a graph of the function.
Write an equation for a function that is the reciprocal of a quadratic and has the following properties:
y = 0
.x = -4
and x = 5
x < -4
and x > 5
, y < 0
Determine an equation for the horizontal asymptote of each function.
\displaystyle
a(x) = \frac{x}{x + 5}
Determine an equation for the horizontal asymptote of each function.
\displaystyle
f(x) = -\frac{2x}{x- 3}
Determine an equation for the horizontal asymptote of each function.
\displaystyle
f(x) = \frac{x + 2}{x-2}
Summarize the key features of each function. Then, sketch a graph of the function.
\displaystyle
f(x) = \frac{x}{x -2}
Summarize the key features of each function. Then, sketch a graph of the function.
\displaystyle
f(x) = - \frac{3x}{x + 1}
Summarize the key features of each function. Then, sketch a graph of the function.
\displaystyle
f(x) = \frac{x-2}{x+ 4}
Summarize the key features of each function. Then, sketch a graph of the function.
\displaystyle
f(x) = \frac{6x+ 2}{2x-1}
Write an equation of a rational function of the
form f(x) = \frac{ax + b}{cx + d}
whose graph has all of the
following features:
\frac{1}{4}
-\frac{1}{2}
x = - \frac{2}{3}
x = \frac{4}{3}
Solve algebraically.
\displaystyle
\frac{7}{x-4} =2
Solve algebraically.
\displaystyle
\frac{3}{x^2 + 6x -24} =1
You can use a graphing device for this. Solve for x.
\displaystyle
\frac{x^2 -3x + 1}{2 -x} =\frac{x^2 + 5x + 4}{x-6}
Solve for x.
\displaystyle
\frac{3}{x + 5} < 2
Solve for x.
\displaystyle
\frac{3}{x + 2} \leq \frac{4}{x + 3}
Solve for x.
\displaystyle
\frac{x^2 -x -20}{x^2 -4x -12} > 0
Solve for x.
\displaystyle
\frac{x}{x + 5} > \frac{x - 1}{x + 7}
Solve for x
.
\displaystyle
\frac{x^2 + 5x +4}{x^2 -5x + 6} < 0
Solve for x
.
\displaystyle
\frac{x^2 -6x + 9}{2x^2 + 17x + 8} > 0
A manufacturer is predicting profit, P, in thousands of dollars. on the sale of x tonnes of fertilizer according to the equation
\displaystyle
P(x) = \frac{600x - 15000}{x + 100}
a) Sketch a graph of this relation.
b) Describe the predicted profit as sales increase.
c) Compare the rtes of change of the profit at sales of 100 t and 500 t of fertilizer.
Sketch a graph of each function. Describe each special case.
\displaystyle
f(x) = \frac{x}{x^2 + 5x}
Sketch a graph of each function. Describe each special case.
\displaystyle
f(x) = \frac{x^2 -2x - 35}{x^2 -3x - 28}