Rational Functions

Front

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

Back

The domain is \( D : (-\infty, -3) \cup (-3, \infty) \) because the function is undefined at \( x = -3 \).

Front

What is the range of the rational function \( f(x) = \frac{1}{x+3} \)?

Back

The range is \( R : (-\infty, 0) \cup (0, \infty) \) because the function never reaches 0.

Front

What is an asymptote?

Back

An asymptote is an imaginary line that your function never touches.

Tags

CCSS.HSF-IF.C.7D

Front

What is the horizontal asymptote of the function \( f(x) = \frac{2x^2 + 3}{x^2 + 1} \)?

Back

The horizontal asymptote is \( y = 2 \) as \( x \) approaches infinity.

Tags

CCSS.HSF-IF.C.7D

Front

Solve for \( x \) using the LCD: \( \frac{1}{x-1} + \frac{1}{x+1} = 1 \)

Back

The solution is \( x = 0 \).

Tags

CCSS.HSA.REI.A.2

Front

What is the vertical asymptote of the function \( f(x) = \frac{1}{x-2} \)?

Back

The vertical asymptote is at \( x = 2 \) because the function is undefined at this point.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean for a function to be undefined?

Back

A function is undefined at points where the denominator is zero.

Tags

CCSS.HSF-IF.C.7D

Front

What is the domain of the function \( f(x) = \frac{1}{x^2 - 4} \)?

Back

The domain is \( D : (-\infty, -2) \cup (-2, 2) \cup (2, \infty) \) because the function is undefined at \( x = -2 \) and \( x = 2 \).

Front

What is the range of the function \( f(x) = \frac{1}{x^2 - 4} \)?

Back

The range is \( R : (-\infty, 0) \) because the function never reaches 0.

Front

What is the significance of the horizontal asymptote?

Back

The horizontal asymptote indicates the behavior of the function as \( x \) approaches infinity.

Tags

CCSS.HSF-IF.C.7D