Introduction to Rational Functions: 동영상 및 연습문제

Identify the domain and range of the following function:

f(x) = 14/x

Identify whether the function f(x) = 3/x⁴ is even or odd, and tell something about its symmetry.

Consider the given rational function and find its domain. 

f(x) = (x +5)/(x² +25)

Complete the given statement using the graph of the rational function in the figure shown. 

As x → -16⁺, f(x) →

Consider the given rational function and find vertical asymptotes and values of x corresponding to holes(if applicable). 

f(x) = x/(x +7)

For the following function, write the coordinates of the hole.

f(x) = (x² - 36)/(x + 6)

Consider the given rational function and find vertical asymptotes and values of x corresponding to holes(if applicable). 

f(x) = (x² -2x -15)/(x +3)

For the given rational function, find out the equation of the horizontal asymptote (if applicable). f(x) = 5x/(2x² +7)

For the following function, write the equations for the vertical, horizontal or oblique asymptotes.

f(x) = (x² + 16)/(x² + 25)

Graph the given rational function using the transformation of f(x) = 1/x², g(x) = 1/x² -11

Graph the given rational function g(x) = 1/(2x+1)² using transformation of f(x) = 1/x²

For the graph of the rational function given below, identify any vertical, horizontal, or oblique asymptotes. Also, write the domain of the function.

Graph the given rational function following the seven steps. f(x)=(7x²-6x−16)/(4x²−5x)

Rewrite the equation of f in the form quotient + remainder/divisor using long division, and graph the function using the equation of this function and the transformation of 1/x.

f(x) = (3x +5)/(x +8)

Solve the given problem using the four-step procedure.

y varies directly as x. y = 72 where x = 12. Find y where x = 17.

Which of the following is a rational function?

What is the domain of the rational function f(x) = (x + 3) / (x^2 - 4)?

Express the domain restrictions of the function f(x) = (x^2 + 5) / (x - 5) in set notation.

Determine the domain restrictions for the function f(x) = (2x + 1) / (x^2 - x - 6).

Simplify the rational function f(x) = (x^2 - 4) / (x^2 - x - 12).

Why is it important to find the domain of a rational function before simplifying?

Let $f\left(x\right)=\frac{7}{2x-9}$. Find the value of $x$ that must be excluded from the domain.

Let $g\left(x\right)=\frac{x+1}{x^2-6x-7}$. Find the smaller value that must be excluded from the domain.

For $h\left(x\right)=\frac{x^2-5x}{x^2-25}$, a factor cancels when simplifying. Find the removable domain restriction (the $x$-value that becomes a hole).

Consider $r\left(x\right)=\frac{x^2+x-6}{x^2-9}$. After fully simplifying, one restriction remains nonremovable. Find the $x$-value of the vertical asymptote.

Simplify $\frac{2x^2-8x}{x^2-4}$ to lowest terms, then find the smaller excluded value from the original domain. Give the excluded value (not the simplified expression).

Let $k\left(x\right)=\frac{x-4}{(x+2)(x-7)}$. Find the larger value excluded from the domain.