Purchase this Material for $14

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

Solutions
38 Videos

Determine equations for the vertical and horizontal asymptotes of each function.

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

Buy to View

Q1a

Determine equations for the vertical and horizontal asymptotes of each function.

```
\displaystyle
f(x) = \frac{3}{x+7}
```

Buy to View

Q1b

Determine equations for the vertical and horizontal asymptotes of each function.

```
\displaystyle
f(x) = -\frac{4}{x-7}
```

Buy to View

Q1c

Determine an equation to represent each function.

Buy to View

Q2a

Determine an equation to represent each function.

Buy to View

Q2b

Sketch a graph of each function. State the domain, range, y-intercepts, and equations of the asymptotes.

```
\displaystyle
f(x) = \frac{5}{x-3}
```

Buy to View

Q3a

Sketch a graph of each function. State the domain, range, y-intercepts, and equations of the asymptotes.

```
\displaystyle
g(x) = -\frac{1}{x-4}
```

Buy to View

Q3b

Sketch a graph of each function. State the domain, range, y-intercepts, and equations of the asymptotes.

```
\displaystyle
h(x) = \frac{1}{2x-3}
```

Buy to View

Q3c

```
\displaystyle
h(x) = - \frac{8}{5x+4}
```

Buy to View

Q3d

Determine equations for the vertical asymptotes of the function. Then, state the domain.

```
\displaystyle
f(x) = \frac{1}{(x -3)(x+ 4)}
```

Buy to View

Q4a

Determine equations for the vertical asymptotes of the function. Then, state the domain.

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

Buy to View

Q4b

Determine equations for the vertical asymptotes of the function. Then, state the domain.

```
\displaystyle
f(x) = \frac{1}{x^2 + 8x + 12}
```

Buy to View

Q4c

,For each function,

- i) determine equations for the asymptotes
- ii) determine the y-intercepts
- iii) sketch a graph
- iv) describe the increasing and decreasing intervals
- v) state the domain and range

```
\displaystyle
f(x) = \frac{1}{x^2 + 6x + 5}
```

Buy to View

Q5a

,For each function,

- i) determine equations for the asymptotes
- ii) determine the y-intercepts
- iii) sketch a graph
- iv) describe the increasing and decreasing intervals
- v) state the domain and range

```
\displaystyle
f(x) = \frac{1}{x^2 - 5x-24}
```

Buy to View

Q5b

,For each function,

- i) determine equations for the asymptotes
- ii) determine the y-intercepts
- iii) sketch a graph
- iv) describe the increasing and decreasing intervals
- v) state the domain and range

```
\displaystyle
f(x) = -\frac{1}{x^2 -6x + 9}
```

Buy to View

Q5c

,For each function,

- i) determine equations for the asymptotes
- ii) determine the y-intercepts
- iii) sketch a graph
- iv) describe the increasing and decreasing intervals
- v) state the domain and range

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

Buy to View

Q5d

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.

Buy to View

Q6

Write an equation for a function that is the reciprocal of a quadratic and has the following properties:

- The horizontal asymptote is
`y = 0`

. - The vertical asymptotes are
`x = -4`

and`x = 5`

- For the intervals
`x < -4`

and`x > 5`

,`y < 0`

Buy to View

Q7

Determine an equation for the horizontal asymptote of each function.

```
\displaystyle
a(x) = \frac{x}{x + 5}
```

Buy to View

Q8a

Determine an equation for the horizontal asymptote of each function.

```
\displaystyle
f(x) = -\frac{2x}{x- 3}
```

Buy to View

Q8b

Determine an equation for the horizontal asymptote of each function.

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

Buy to View

Q8c

Summarize the key features of each function. Then, sketch a graph of the function.

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

Buy to View

Q9a

Summarize the key features of each function. Then, sketch a graph of the function.

```
\displaystyle
f(x) = - \frac{3x}{x + 1}
```

Buy to View

Q9b

Summarize the key features of each function. Then, sketch a graph of the function.

```
\displaystyle
f(x) = \frac{x-2}{x+ 4}
```

Buy to View

Q9c

Summarize the key features of each function. Then, sketch a graph of the function.

```
\displaystyle
f(x) = \frac{6x+ 2}{2x-1}
```

Buy to View

Q9d

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:

- x-intercept of
`\frac{1}{4}`

- y-intercept of
`-\frac{1}{2}`

- vertical asymptote with equations
`x = - \frac{2}{3}`

- horizontal asymptote with equations
`x = \frac{4}{3}`

Buy to View

Q10

Solve algebraically.

```
\displaystyle
\frac{7}{x-4} =2
```

Buy to View

Q11a

Solve algebraically.

```
\displaystyle
\frac{3}{x^2 + 6x -24} =1
```

Buy to View

Q11b

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}
```

Buy to View

Q12c

Solve for x.

```
\displaystyle
\frac{3}{x + 5} < 2
```

Buy to View

Q13a

Solve for x.

```
\displaystyle
\frac{3}{x + 2} \leq \frac{4}{x + 3}
```

Buy to View

Q13b

Solve for x.

```
\displaystyle
\frac{x^2 -x -20}{x^2 -4x -12} > 0
```

Buy to View

Q13c

Solve for x.

```
\displaystyle
\frac{x}{x + 5} > \frac{x - 1}{x + 7}
```

Buy to View

Q13d

Solve for `x`

.

```
\displaystyle
\frac{x^2 + 5x +4}{x^2 -5x + 6} < 0
```

Buy to View

Q14a

Solve for `x`

.

```
\displaystyle
\frac{x^2 -6x + 9}{2x^2 + 17x + 8} > 0
```

Buy to View

Q14b

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.

Buy to View

Q15

Sketch a graph of each function. Describe each special case.

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

Buy to View

Q16a

Sketch a graph of each function. Describe each special case.

```
\displaystyle
f(x) = \frac{x^2 -2x - 35}{x^2 -3x - 28}
```

Buy to View

Q16b