Graph Transformation and Function Domain Quiz

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Questions and Answers

Which of the following is an equation for g(x) in terms of f(x)?

  • $g(x) = f(x^2 + 1) + 10$
  • $g(x) = 2f(2x)$
  • $g(x) = 2f(x^2 + 1)$
  • $g(x) = f(2x) + 10$ (correct)

If Point A(-3, 4) is on the graph of $y = f(x)$, then the corresponding image point, A', on the graph of $y = f(2x) + 3$ is?

  • (3, 1)
  • (-5, 1) (correct)
  • (-5, 7)
  • (3, 7)

How many points would be invariant when the graph of $y = f(x)$ is reflected in the line $y = x$?

  • 2 (correct)
  • Infinitely many
  • 1
  • 0

What is the domain and range of the transformed function $y = f(2x) + 1$?

<p>$\text{Domain: } x eq 4, 1; \text{ Range: } y eq -8, 4$ (D)</p>
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An equation for $g(x)$ in terms of $f(x)$ after a transformation is $y = f(2x) + 10$. What is the corresponding point P' on the graph of $y + 3 = f(2x) + 1$?

<p>(4,5) (A)</p>
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Who created the earliest-known tables of values for trigonometric ratios?

<p>Mathematicians in India (C)</p>
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In which century did the field of trigonometry emerge?

<p>3rd century BC (A)</p>
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What method did the Sumerian astronomers use to study angle measure?

<p>Division of circles into 360 degrees (A)</p>
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What are trigonometric identities commonly used for?

<p>To simplify trigonometrical expressions (D)</p>
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What areas have trigonometry been applied in throughout history?

<p>Geodesy, surveying, celestial mechanics, and navigation (D)</p>
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