3.4 Assessment for Grading Unit 3 Curve Sketching PDF

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Summary

1.a.b.2.a.The domain of the function isThe function is neitherc.The function is odd a. The vertical asymptotes are x = 7 and x = - b.The vertical asymptotes are x = -1 ; x = -3 and x = 2 a. Since the polynomial in the numerator is a bigger deghorizontal asymptote. ree than the denominator, there is ...

Description

1. a.

b.

2. a.

The domain of the function

is

b.

The domain of the function

is

c.

The domain of the function

is

3. a.

The function b.

is even

The function

is neither

c.

The function

is odd

4. a.

The vertical asymptotes are x = 7 and x = -4 b.

The vertical asymptotes are x = -1 ; x = -3 and x = 2

5. a.

Since the polynomial in the numerator is a bigger degree than the denominator, there is no horizontal asymptote.

b.

Since the polynomial in the numerator is a lower degree than the denominator, y = 0 is the horizontal asymptote.

c.

Since the numerator and denominator have the same degree

The horizontal asymptote is y = 2

6. a. i)

The critical value is

ii) The intervals

Intervals

2x + 3

4(2x+3)

Increasing or decreasing

-

-

Decreasing

+

+

Increasing

The function

is increasing on the interval

The function

is decreasing on the interval

iii)

Since the function changes from decreasing to increasing at the value

minimum point at

b. i)

. The minimum point is

, there is a

.

The critical values are 2 and 4

ii) Intervals

Intervals

x-2

x-4

3(x - 2)(x - 4)

Increasing or decreasing

x 1

The function

is concave down on the intervals -1 < x < 1

Points of inflection

Since the function changes from concave down to concave up at x = -1, there could be an inflection point at = −1 . However, = −1 is a restriction on the domain. There is no point of inflection at x = -1. Since the function changes from concave up to concave down at x = 1, there could be an inflection point at = 1 . However, = 1 is a restriction on the domain. There is no point of inflection at x = 1. Therefore, there is no point of reflection Sketch the curve...