MHF4U Rational Functions Practice Test
1. [6K] Given
determine the equations of all asymptotes, coordinates of hole(s), y-
intercept and zeros.
2. [4K] Solve
without the use of a graphing calculator. Show all work.
3. [2K] Is this the graph of a reciprocal function of a linear or a quadratic function? Explain how you know.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
4. [2K, 2A] This is the graph of
f(x)
and
. For what interval(s) is
g(x)?
y
x
5. [3A] State the equation of a rational function if the vertical asymptote is x = 5, the horizontal asymptote is y =
2, the x-intercept is
and the y-intercept is
.
6. [2A] Mrs.Rivenell says that the average rate of change between x = -6 and x = -3 for the function
is 0.5. Mr.Blakely disagrees. With whom do you side and why?
7. At a small clothing company, the estimated cost function for producing a new line of jeans is
C(x) =
, where x is the number of pairs of jeans produced, in thousands. C(x) is measured in dollars.
a. [1K] Calculate the cost of a pair of jeans at a production level of 3000 pairs.
b. [3K] Determine the rate at which the cost is changing at a production level of 3000 pairs of jeans using any
method. Show all work.
8. [4A] Given y = f(x) and the equations of the vertical and horizontal asymptotes. Determine a possible
equation. Show all work. Graph is NOT to scale. Solution must be independent of a graphing calculator.
y
5
4
(5, 3)
3
2
1
–14 –12 –10 –8
–6
–4
–2
–1
–2
–3
–4
–5
(1, 0)
2
4
6
8
10
12
14
16
18
20
x