Modelling Curves using Logarithms

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Modelling Curves using Logarithms Revision Questions

1. . Which of the following is NOT a function?

1. x² + y² = 9
2. x + y = 9
3. x² + y = 9
4. x · y = 9

Reveal AnswerCorrect Answer: A

2. . Which of the following figures does NOT show the graph of a function?

Reveal AnswerCorrect Answer: C

3. . Which of the following exponential functions has a graph with an opposite orientation to the other three?

1. y(x) = 2 · 5^x
2. y(x) = ½ · 4^x
3. y(x) = 3 · 2^x
4. y(x) = 4 · (1/2)^x

Reveal AnswerCorrect Answer: D

4. . What is the value of the coefficient k in the exponential function y(x) = k · a^x shown by the graph below?

1. 0
2. 1
3. 2
4. 3

Reveal AnswerCorrect Answer: C

5. . What is the base b of the function y(x) = k · b^x shown in the figure below?

1. 4
2. 5
3. 6
4. 7

Reveal AnswerCorrect Answer: B

6. . Which of the following graphs does NOT show a logarithmic function?

Reveal AnswerCorrect Answer: D

7. . What is the logarithmic function indicated by the graph below?

1. y(x) = log x
2. y(x) = log₃ x
3. y(x) = 3 log x
4. y(x) = log (x/3)

Reveal AnswerCorrect Answer: C

8. . What is the value of b for the logarithmic function y(x) = b · log x indicated by the graph below?

1. -4
2. -2
3. 2
4. 4

Reveal AnswerCorrect Answer: A

9. . A modelled curve of the function y(x) = k · xn is shown in the graph below.

What is the value of the exponent n?

1. 2
2. 3
3. 4
4. 5

Reveal AnswerCorrect Answer: B

10. . A modelled curve of the function y(x) = k · xⁿ is shown in the graph below.

What is the value of the coefficient k?

1. 1
2. 2
3. 5
4. 9

Reveal AnswerCorrect Answer: A

11. . Which of the following lines represent the function y(x) = 3x² after modelling the curve?

1. log y = log 3x + 2 log x
2. log y = log 3 + 2 log x
3. log y = log 3 + x log 2
4. log y = log 3 + log x + log 2

Reveal AnswerCorrect Answer: B

12. . Which of the following lines represent the function y(x) = 0.5 · 4^x after modelling the curve?

1. log y = log 2 + x log 4
2. log y = x log 4 - log 2
3. log y = log 0.5 + 4 log x
4. log y = log 0.5 - x log 4

Reveal AnswerCorrect Answer: B

13. . What is the equation of the line obtained after modelling the curve of the function shown by the data below?

1. y(x) = 0.6 x²
2. log y = log 15 - 2 log x
3. log y = 0.6 log x + log 2
4. log y = 2 log x - log 6

Reveal AnswerCorrect Answer: D

14. . What is the equation of the line obtained after modelling the curve of the function shown by the data below?

1. y = 1.2 · 5^x
2. log y = log 1.2 + x · log 5
3. y = 1.2 + 5x
4. log y = log 1.2 + 5 log x

Reveal AnswerCorrect Answer: B

15. . What is the original function shown by the table below used for modelling the curve?

1. y(x) = 3^-2x
2. y(x) = -3x^-2
3. y(x) = -3x²
4. y(x) = -3 · 2^x

Reveal AnswerCorrect Answer: D

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6. Continuing learning logarithms - read our next math tutorial: Natural Logarithm Function and Its Graph

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