For mathguru
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Math 30-1 – Unit 7: Radical and Rational Functions Assignment
Name: _____________________________ /33 Marks
If your name does not appear in your writing on the hardcopy scan – you will lose one mark!
1. Identify the transformations for from 𝑦 = √𝑥 /2
2. Write the equation of the radical function that results from the following transformations on
the graph of 𝑦 = √𝑥 in the order presented. a. Vertical stretch by a factor of four, reflection in the x axis, horizontal stretch by a factor of
one-sixth and a translation 5 units left and 1 unit up. (2 marks)
b. Horizontal stretch by a factor of one third, reflection in the y axis, horizontal translation
4 units left. (1 mark)
3. Write the equation of each of the following. Use the form 𝑦 = 𝑎 √𝑏(𝑥 − ℎ) + 𝑘.
(3marks each)
a. b.
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4. Given the graph of y = f (x) graph the function that would represent 𝑦 = √𝑓 (𝑥). List the
domain and range of each graph, list the EXACT VALUES of any invariant points.
5. Solve each of the following algebraically for their exact values. (1 mark each)
a. b.
6. What vertical stretch is applied to 𝑦 = √2𝑥 + 1 , if the transformed graph passes through (4, 18)? (1 mark)
7. As a result of the transformation of 𝑦 = √𝑥 into the graph of 2𝑦 = √𝑥 + 1 , the point P(64, 8) is transformed to (a, b). Determine the coordinates of the point (a, b). (2 marks)
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8. Sketch the graphs of and show all asymptotes with a dotted line. /1
a. Equation of any vertical asymptote(s)
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b. State any restrictions or non-
permissible value(s)
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c. Determine coordinates of any
intercept(s). (algebraically)
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d. State the horizontal asymptote
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e. State the Domain and Range
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9. Write a possible equation for the following graph. Explain your reasoning.
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10. Determine the coordinates of the point of discontinuity on the graph of
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11. The equations of seven rational functions and the graphs of these functions are shown. If a,
b, and c are distinct natural numbers, match the set of rational functions to their graphs and
explain the reasoning.
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