Hyperbola & Exponential Graphs (Grade 11) — Worksheet & Memo

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Grade 11 · Functions and Graphs

Hyperbola & Exponential Graphs (Grade 11)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 23

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Write down the asymptotes of y = 4/(x − 1) + 2.
(2)
x = 1 and y = 2✓✓ (2)
2
Determine the y-intercept of y = 4/(x − 1) + 2.
(2)
4/−1 + 2 = −2✓✓ (2)
3
Determine the x-intercept of y = 4/(x − 1) + 2.
(3)
4 = −2(x − 1) → x = −1✓✓✓ (3)
4
Write down the domain and range of y = 4/(x − 1) + 2.
(2)
Domain x ∈ ℝ, x ≠ 1; range y ∈ ℝ, y ≠ 2✓✓ (2)
5
Write down the equation of the asymptote of y = 2^x − 1.
(1)
y = −1✓ (1)
6
Determine the y-intercept of y = 2^x − 1.
(2)
2⁰ − 1 = 0✓✓ (2)
7
Write down the range of y = 2^x − 1.
(1)
y > −1✓ (1)
8
Describe the transformation from y = 2^x to y = 2^x − 1.
(2)
A translation of 1 unit downwards✓✓ (2)
9
For y = 2^{x − 3} + 1, write down the equation of the asymptote and describe the transformation from y = 2^x.
(3)
Asymptote y = 1 ✓; the graph is shifted 3 units RIGHT ✓ and 1 unit UP ✓(3)
10
Determine the y-intercept of y = 4 · 3^{x + 1} − 5.
(3)
x = 0: y = 4 × 3¹ − 5 ✓ = 12 − 5 ✓ = 7 ✓(3)
11
Explain why the value of p does NOT change the horizontal asymptote of an exponential graph.
(2)
p is a horizontal shift ✓; the asymptote is a horizontal line whose height is set by q only, so sliding the graph sideways leaves it at y = q ✓(2)

TOTAL: 23 marks