What is the domain of the function $$f(x) = \frac{1}{x+3} - 5$$ ?

The domain of the function is all real numbers except where the denominator is zero. For $$f(x) = \frac{1}{x+3} - 5$$ , the domain is all real numbers except $$x = -3$$ .

How do you determine the horizontal asymptote of the function $$f(x) = \frac{1}{x+3} - 5$$ ?

For the function $$f(x) = \frac{1}{x+3} - 5$$ , as x approaches infinity, $$f(x)$$ approaches -5. Therefore, the horizontal asymptote is $$y = -5$$ .

What are the coordinates of the point on the unit circle at an angle of $$\frac{\theta}{2}$$ ?

The coordinates of the point on the unit circle at an angle $$\theta$$ are given by $$(\text{cos}(\theta), \text{sin}(\theta))$$ .

What is the relationship between the unit circle and trigonometric functions?

The unit circle provides a geometric interpretation of the sine and cosine functions, where the x-coordinate represents cosine and the y-coordinate represents sine for a given angle.

How do you find the sine and cosine of common angles (0, 30, 45, 60, 90 degrees)?

Using the unit circle: - $$0^\text{°}$$ : (1, 0) - $$30^\text{°}$$ : (√3/2, 1/2) - $$45^\text{°}$$ : (√2/2, √2/2) - $$60^\text{°}$$ : (1/2, √3/2) - $$90^\text{°}$$ : (0, 1)

What is the significance of the angle in radians on the unit circle?

Angles in radians correspond to the arc length on the unit circle. For example, an angle of $$\frac{\theta}{2}$$ radians corresponds to an arc length of $$\frac{\theta}{2}$$ units.

What is the formula for converting degrees to radians?

To convert degrees to radians, use the formula: $$\text{radians} = \text{degrees} \times \frac{\text{π}}{180}$$ .

What is the period of the sine and cosine functions?

The period of the sine and cosine functions is $$2\text{π}$$ , meaning they repeat their values every $$2\text{π}$$ radians.

How do you graph a rational function?

To graph a rational function, identify the vertical and horizontal asymptotes, find intercepts, and plot points to understand the behavior of the function.

What is the effect of shifting a function vertically?

Shifting a function vertically involves adding or subtracting a constant from the function. For example, $$f(x) = \frac{1}{x+3} - 5$$ shifts the graph of $$\frac{1}{x+3}$$ down by 5 units.

What is the significance of the x-intercept of a function?

The x-intercept of a function is the point where the graph crosses the x-axis, indicating the value of x for which the function equals zero.

Alg 2 - Unit 6 & 7 Exam Review (Rational Fun. & Unit Circle) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a rational function?

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

How do you find the vertical asymptote of a rational function?

Back

To find the vertical asymptote of a rational function, set the denominator equal to zero and solve for x. The vertical asymptote occurs at the values of x that make the denominator zero.

4.

FLASHCARD QUESTION

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity. It indicates the behavior of the function at extreme values of x.

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the unit circle?

Back

The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane. It is used to define trigonometric functions.

7.

FLASHCARD QUESTION

Front

Back

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