📝 Chapter 3: Rational Functions

Assessment AS Learning — Practice Quiz

🔄 Not Graded — Unlimited Retakes

Purpose: Self-check your understanding. This quiz is not graded. Click "Check Answer" for instant feedback and "Show Solution" for detailed explanations with rendered formulas.

Score: 0 / 5

3.2 — Reciprocal of Linear Functions

Question 1

The vertical asymptote of \( f(x) = \frac{1}{x-3} \) is:

\( x = 3 \)
\( x = -3 \)
\( y = 3 \)
\( y = 0 \)

Solution:

Set denominator = 0: \( x - 3 = 0 \Rightarrow x = 3 \). VA is a vertical line \( x = 3 \).

Question 2

The horizontal asymptote of \( f(x) = \frac{1}{x-3} \) is:

\( y = 0 \)
\( y = 1 \)
\( y = 3 \)
\( y = -3 \)

Solution:

As \( x \to \pm\infty \), \( \frac{1}{x-3} \to 0 \). The HA is \( y = 0 \).

3.4 — Linear over Linear

Question 3

For \( f(x) = \frac{2x+1}{x-3} \), the horizontal asymptote is:

\( y = 2 \)
\( y = \frac{1}{3} \)
\( y = -\frac{1}{3} \)
\( y = 0 \)

Solution:

For \( \frac{ax+b}{cx+d} \), the HA is \( y = \frac{a}{c} = \frac{2}{1} = 2 \).

Question 4

What is the y-intercept of \( f(x) = \frac{2x+1}{x-3} \)? Express as a decimal.

Solution:

\( f(0) = \frac{2(0)+1}{0-3} = \frac{1}{-3} = -\frac{1}{3} \approx -0.33 \)

3.6 — Rational Equations

Question 5

Solve: \( \frac{3}{x-1} = \frac{5}{x+2} \). What is \( x \)?

Solution:

Cross multiply: \( 3(x+2) = 5(x-1) \)
\( 3x + 6 = 5x - 5 \)
\( 11 = 2x \)
\( x = \frac{11}{2} = 5.5 \)

MHF4U — Advanced Functions, Grade 12 | Ontario Curriculum 2007 (Revised)
C. Polynomial and Rational Functions
Assessment AS Learning — Self-Directed, Not Graded