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  2. AP Pre Calculus
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Polynomial and Rational Functions

Question 1
college-boardPre-CalculusAPExam Style
1 mark

What value can be excluded from the domain of f(x)=5x+3f(x) = \frac{5}{x + 3}f(x)=x+35​?

Question 2
college-boardPre-CalculusAPExam Style
1 mark

Given two rational functions R1(x)=ax+bcx+dR_1(x)=\frac{ax+b}{cx+d}R1​(x)=cx+dax+b​ & R2(y)=ey+fgy+hR_2(y)=\frac{ey+f}{gy+h}R2​(y)=gy+hey+f​, if R1(10)=R2(10)R_1(10)=R_2(10)R1​(10)=R2​(10) and a=ea=ea=e and b=fb=fb=f and c=gc=gc=g and d≠hd \neq hd=h, then what can we conclude about their graphs?

Question 3
college-boardPre-CalculusAPExam Style
1 mark

Given g(x)=x5−4(x6+10)23g(x)=\frac{x^{5}-4}{(x^{6}+10)^{\frac{2}{3}}}g(x)=(x6+10)32​x5−4​; how would you describe g(x)g(x)g(x)'s behaviour as 'x' nears negative infinity?

Question 4
college-boardPre-CalculusAPExam Style
1 mark

What is the end behavior of the rational function f(x)=2x3x2−4f(x) = \frac{2x^3}{x^2-4}f(x)=x2−42x3​ as x approaches infinity?

Question 5
college-boardPre-CalculusAPExam Style
1 mark

What is the end behavior of the rational function f(x)=3x2x−4f(x) = \frac{3x^2}{x-4}f(x)=x−43x2​ as xxx approaches infinity?

Question 6
college-boardPre-CalculusAPExam Style
1 mark

What type of discontinuity is present at a point where a function has an asymptote?

Question 7
college-boardPre-CalculusAPExam Style
1 mark

For which value(s) does the vertical asymptote occur in the function defined by g(x)=x+3(x−1)(x+4)?g(x)=\frac{x+3}{(x-1)(x+4)}?g(x)=(x−1)(x+4)x+3​?

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Question 8
college-boardPre-CalculusAPExam Style
1 mark

Question #4: Which transformation could turn an oblique asymptote into a horizontal or vertical one when applied to a rational function with higher-degree terms in its numerator than its denominator?

Question 9
college-boardPre-CalculusAPExam Style
1 mark

What happens to the values of f(x)=3−xxf(x) = \frac{3-x}{x}f(x)=x3−x​ as xxx approaches the vertical asymptote from the right?

Question 10
college-boardPre-CalculusAPExam Style
1 mark

If a rational function has a horizontal asymptote at y=2y = 2y=2, what does yyy approach as xxx goes to infinity?