Problem

1. Sketch each pair of functions on the same set of axes. Include all axes intercepts and asymptotes. - i

y = x^2

and

y = \frac{1}{x^2}

- ii

y = -(x - 1)^2

and

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

- iii

y = x^2 + 4

and

y = \frac{1}{x^2 + 4}

- iv

y = -(x^2 - 4)

and

y = -\frac{1}{x^2 - 4}

- v

y = (x - 1)(x - 3)

and

y = \frac{1}{(x - 1)(x - 3)}

2. How can the vertical asymptotes of

y = \frac{1}{f(x)}

be established from

f(x)

without first viewing its graph? 3. What other observations can you make about the graph of

y = \frac{1}{f(x)}

? a. Sketch each pair of functions on the same set of axes. Include all axes intercepts and asymptotes. - i

y = x^2

and

y = \frac{1}{x^2}

- ii

y = -(x - 1)^2

and

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

- iii

y = x^2 + 4

and

y = \frac{1}{x^2 + 4}

- iv

y = -(x^2 - 4)

and

y = -\frac{1}{x^2 - 4}

- v

y = (x - 1)(x - 3)

and

y = \frac{1}{(x - 1)(x - 3)}