Rational Functions: Domain & Range

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Domain and range basics

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John Lexian Pereña

Philippines

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Rational Functions: Domain & Range


Froggy Jumps Rational Functions: Domain & RangeOnline version Domain and range basics by John Lexian Pereña 1 What is the first step to find the domain of a rational function f(x)=P(x)/Q(x)? a Set f(x) to zero and solve for x b Find x-values that do not make Q(x)=0 c Find zeros of P(x) 2 If Q(x)=0 at x=3, what is true about the domain of f(x)=P(x)/Q(x)? a x ≥ 3 b x = 3 c x ≠ 3 3 A rational function has a hole where which condition holds? a P and Q share a common factor that cancels b Q has a repeated root c P is zero for all x 4 How would you find the range of a simple rational function? a Set x to 0 and compute y b Solve y = P(x)/Q(x) for x and determine real x where defined c Check only horizontal asymptotes 5 What can cause a horizontal asymptote in a rational function? a Degrees of P and Q provide a ratio b P has higher degree than Q by 2 c P and Q have same zeros 6 Consider f(x)=1/(x-2). What is its domain? a All real numbers except x=2 b All real numbers except x=0 c All real numbers 7 For f(x)= (x^2-1)/(x^2-4), what are the x-values excluded from the domain? a x=±1 b x=±2 c x=0 8 If f(x)=(x-3)/(x^2-5x+6), which x are not in the domain? a x=0 and x=1 b x=2 and x=3 c x=5 and x=6 9 Which statement about the range of a rational function is often true? a The range always includes all real numbers b The range may exclude values due to horizontal/oblique asymptotes c The range is always finite 10 When a rational function is simplified and a hole remains, what happens to the domain and range near the hole? a Domain excludes the hole; the function approaches a finite limit affecting y-values b Domain excludes the hole; range becomes all real numbers c Domain is all reals; hole has no effect on range 11 For f(x)= (x+3)/(x-2), what is the domain of f? a x= -3 only b All real numbers except x=2 c All real numbers 12 What is the range of f(x)=(x+3)/(x-2) a All real numbers except y=1 b y= -1 only c All real numbers 13 If g(x)=(x^2-4)/(x-2), which X-value is excluded from the domain? a x=2 b x=0 c x=-2 14 A rational function R(x)=(2x+1)/(x^2-1) has domain excluding which x-values? a x=2 and x=-2 b x=0 and x=1 c x=1 and x=-1 15 Which transformation can create a hole in the graph of a rational function? a Canceling a common factor between numerator and denominator b Multiplying only by x c Adding a constant term 16 For h(x)=(x^2-9)/(x-3), what is the domain? a All real numbers b All real numbers except x=3 c All real numbers except x=-3 17 What is the range of y=(x-4)/(x+2) as x approaches -2 from either side? a All real y values except y= -1 b All real numbers c y=1 only 18 If p(x)=(x^2+2x+1)/(x-1), is there a vertical asymptote, and if so where? a Yes, at x=-1 b No vertical asymptote c Yes, at x=1 19 Given q(x)=(3x-6)/(2x-4), which value is excluded from the domain? a x=1 b x=0 c x=2/3 20 For r(x)=(x^3-1)/(x-1), what is the domain after simplification? a All real numbers except x=1 b All real numbers except x=-1 c All real numbers

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Rational Functions: Domain & Range

Froggy Jumps

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Rational Functions: Domain & RangeOnline version

by John Lexian Pereña

What is the first step to find the domain of a rational function f(x)=P(x)/Q(x)?

If Q(x)=0 at x=3, what is true about the domain of f(x)=P(x)/Q(x)?

A rational function has a hole where which condition holds?

How would you find the range of a simple rational function?

What can cause a horizontal asymptote in a rational function?

Consider f(x)=1/(x-2). What is its domain?

For f(x)= (x^2-1)/(x^2-4), what are the x-values excluded from the domain?

If f(x)=(x-3)/(x^2-5x+6), which x are not in the domain?

Which statement about the range of a rational function is often true?

When a rational function is simplified and a hole remains, what happens to the domain and range near the hole?

For f(x)= (x+3)/(x-2), what is the domain of f?

What is the range of f(x)=(x+3)/(x-2)

If g(x)=(x^2-4)/(x-2), which X-value is excluded from the domain?

A rational function R(x)=(2x+1)/(x^2-1) has domain excluding which x-values?

Which transformation can create a hole in the graph of a rational function?

For h(x)=(x^2-9)/(x-3), what is the domain?

What is the range of y=(x-4)/(x+2) as x approaches -2 from either side?

If p(x)=(x^2+2x+1)/(x-1), is there a vertical asymptote, and if so where?

Given q(x)=(3x-6)/(2x-4), which value is excluded from the domain?

For r(x)=(x^3-1)/(x-1), what is the domain after simplification?