How do you find the domain of a rational function?

The domain of a rational function is all real numbers except where the denominator equals zero.

What does it mean for a function to be continuous?

A function is continuous if there are no breaks, jumps, or holes in its graph.

What is the effect of subtracting a constant from a function?

Subtracting a constant shifts the graph of the function downward by that constant.

What is the effect of adding a constant to a function?

Adding a constant shifts the graph of the function upward by that constant.

What is the significance of the point where a function is undefined?

The point where a function is undefined may indicate a discontinuity or vertical asymptote.

How do you identify vertical asymptotes in a rational function?

Vertical asymptotes can be identified by setting the denominator equal to zero and solving for x.

What is the range of a function?

The range of a function is the set of all possible output values (y-values) that the function can produce.

What happens to the graph of a function when you shift it left or right?

Shifting a function left or right translates the graph horizontally along the x-axis.

What is the relationship between discontinuities and asymptotes?

Discontinuities can indicate the presence of vertical asymptotes, where the function approaches infinity.

Unit 5 Flashcard 2: 16 Cards (11th Grade)

Student preview

16 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the transformation of the expression $\frac{1}{x}-5$ ?

Back

down 5

2.

FLASHCARD QUESTION

Front

What is the domain and range of the expression $f(x)=\frac{1}{x-3}+2$ ?

Back

Domain: x cannot be 3; Range: y cannot be 2

3.

FLASHCARD QUESTION

Front

State and classify all discontinuities for $j(x)=\frac{x+3}{x^2-x-12}$ .

Back

Removeable Discontinuity at x = -3; VA at x = 4

4.

FLASHCARD QUESTION

Front

What is the transformation of the expression $\frac{1}{x+1}$ ?

Back

left 1

5.

FLASHCARD QUESTION

Front

State and classify all discontinuities for $g(x)=\frac{(3x+4)}{(3x+4)(x+2)}$ .

Back

Removeable Discontinuity at x = -4/3; VA at x = -2

6.

FLASHCARD QUESTION

Front

Define removable discontinuity.

Back

A removable discontinuity occurs when a function is not defined at a point, but can be made continuous by defining it at that point.

7.

FLASHCARD QUESTION

Front

What is a vertical asymptote (VA)?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a.

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