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Dilation of Functions in Algebra

Dilation of Functions in Algebra

Explore the concepts of dilations in functions, including vertical and horizontal transformations. This quiz covers multiplicative behaviors, their impacts on graphs, and the order of transformation applications. Test your understanding of how dilation affects both vertical and horizontal scales in algebra.

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Quiz21 Questions
Flashcards28 Cards
Study Notes1 Note
Podcast1 Episode

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Start with the earlier modules and work forward. Each one builds on the last, so the course gets more advanced as you go.

Dilation of Functions in Algebra

Quiz • 21 Questions

Dilation of Functions in Algebra - Flashcards

Flashcards • 28 Cards

Study Notes

2 min • Summary

Dilation of Functions in Algebra - Podcast

Podcast

Materials

List of Questions21 questions
  1. Question 1
    • The y-values are multiplied by 4 and the x-values are unaffected.
    • The graph is reflected across the x-axis and translated down.
    • The y-values are only increased by 6.
    • The y-values are multiplied by 4 and then increased by 6.
  2. Question 2
    • It compresses the graph horizontally by a factor of 2.
    • It stretches the graph horizontally by a factor of 2.
    • It flips the graph over the y-axis.
    • It translates the graph upward by 2 units.
  3. Question 3
    • The maximum points of the function 𝑔.
    • The x-values where the graph touches the y-axis.
    • The x-values where 𝑔(𝑥) = 0.
    • The y-values where the graph crosses the x-axis.
  4. Question 4
    • The graph will always be a straight line.
    • The function will have no zeroes.
    • The function can still take any real values.
    • The function's output values may not cover the entire range.
  5. Question 5
    • The slope of the function at x=0.
    • The value of g at x=0 directly on the graph.
    • The point where the function approaches infinity.
    • The number of zeroes the function has.
  6. Question 6
    • It shifts the graph horizontally to the left.
    • It compresses the graph vertically.
    • It reflects the graph over the x-axis.
    • It stretches the graph vertically.
  7. Question 7
    • It expands the graph horizontally.
    • It shifts the graph upwards.
    • It compresses the graph horizontally.
    • It stretches the graph vertically.
  8. Question 8
    • [2, 2]
    • [0, 5]
    • [2, 5]
    • [3, 7]
  9. Question 9
    • [1, 6]
    • [4, 9]
    • [7, 12]
    • [0, 6]
  10. Question 10
    • It has a zero at $x = 0$.
    • It has a zero at $x = 1$ and $x = -1$.
    • It has a zero at $x = 1/3$.
    • It has a zero at $x = 1$.
  11. Question 11
    • The y-intercept will be at $(0, 5)$.
    • The x-intercept will shift to $(2, 5)$.
    • The x-intercept will remain at $(2, 0)$.
    • The y-intercept will be at $(0, 20)$.
  12. Question 12
    • Shift 2 units to the right.
    • Shift 1 unit to the left.
    • No horizontal shift.
    • Shift 1 unit to the right.
  13. Question 13
    • Shift to the left 3 units and then down 5 units.
    • Shift down 5 units and then right 3 units.
    • Shift up 5 units and then left 3 units.
    • Shift to the right 3 units and then up 5 units.
  14. Question 14
    • It compresses the graph vertically by a factor of 3 and translates it downward by 5 units.
    • It does not change the graph at all.
    • It reflects the graph across the x-axis and translates it vertically.
    • It stretches the graph vertically by a factor of 3 and translates it upward by 5 units.
  15. Question 15
    • Horizontal shrink by a factor of 3 and vertical shift down by 1.
    • Vertical stretch by a factor of 3 and horizontal shift up by 1.
    • Horizontal stretch by a factor of 3 and vertical shift down by 1.
    • Vertical shrink by a factor of 3 and horizontal shift up by 1.
  16. Question 16
    • The domain of $g(x)$ is $ ext{[0, 4]}$.
    • The domain of $g(x)$ is the same as $f(x)$, $ ext{[a, b]}$.
    • The domain of $g(x)$ is $ ext{(-∞, ∞)}$.
    • The domain of $g(x)$ is $ ext{[a+4, b+4]}$.
  17. Question 17
    • Shift right 2 units and down 3 units.
    • Shift right 2 units and up 3 units.
    • Shift left 2 units and up 3 units.
    • Shift left 2 units and down 3 units.
  18. Question 18
    • $g(x) = -f(x)$
    • $g(x) = f(x) - 4$
    • $g(x) = 2f(x)$
    • $g(x) = f(-x)$
  19. Question 19
    • g(x) has a zero at $x = 3$ after reflection.
    • g(x) has a zero at $x = 0$.
    • g(x) has a zero at $x = 3$.
    • g(x) has a zero at $x = 3$ after translation.
  20. Question 20
    • [2c + 1, 2d + 1]
    • [2c, 2d]
    • [-2d, -2c]
    • [c + 1, d + 1]
  21. Question 21
    • [1, 5]
    • [1, 6]
    • [0, 5]
    • [0, 4]
List of Flashcards28 flashcards
  1. Card 1
    HintThink about how different operations affect the coordinate points on a graphMemory TipVisualize graph transformations
  2. Card 2
    HintThink squeezing or spreading the graph horizontallyMemory TipChange the x values
  3. Card 3
    HintThink squeezing or spreading the graph verticallyMemory TipChange the y values
  4. Card 4
    HintThink moving the graph up or down the y-axis.Memory TipAdd or subtract a value to the y-value
  5. Card 5
    HintOne function acting on the results of another.Memory TipChain reaction
  6. Card 6
    HintTransforms function f, horizontally, then verticallyMemory TipFunction transformation, 3f(2x)
  7. Card 7
    HintUse the function definition and given values.Memory TipSubstitute and compute
  8. Card 8
    HintSolutions to f(x) = 0.Memory TipX-intercepts
  9. Card 9
    HintFind the value of f(0).Memory TipY-axis crossing point
  10. Card 10
    HintThink of multiplying the y-values of the function.Memory TipVertical stretch/squish
  11. Card 11
    HintThink of stretching or shrinking the graph vertically.Memory TipVertical stretch/shrink
  12. Card 12
    HintThink of multiplying the x-values of the function.Memory TipHorizontal stretch/squish
  13. Card 13
    HintInput x is multiplied by 3.Memory TipHorizontal compression x values by 3 times
  14. Card 14
    HintThink of a function as a set of points, not just a graph.Memory TipChange the scale.
  15. Card 15
    HintThink of moving the graph up or down.Memory TipVertical shift up/down
  16. Card 16
    HintLook at the constant in front of the function to determine the transformations.Memory TipMultiples change shapes/sizes.
  17. Card 17
    HintThink of moving the graph left or right.Memory TipHorizontal shift left/right
  18. Card 18
    HintThe output of f(x) is multiplied by 2.Memory TipVertical double.
  19. Card 19
    HintOutputs (y-values) are doubled.Memory TipVertical stretch by 2
  20. Card 20
    HintThe input x values are halved.Memory TipHorizontal squeeze.
  21. Card 21
    HintThink of the 'x' values that are allowed.Memory TipPossible x values
  22. Card 22
    HintThe constant in front of f(x) multiplies the output. The constant at the end shifts the graph vertically.Memory TipVertical stretch + shift up.
  23. Card 23
    HintThink of the 'y' values that result from the function.Memory TipPossible y values
  24. Card 24
    HintThink of the horizontal length of the graph.Memory TipInput X-values.
  25. Card 25
    HintLook for changes inside the parenthesis of the function.Memory TipInside the x
  26. Card 26
    HintThink of the vertical length of the graph.Memory TipOutput Y-values.
  27. Card 27
    HintLook for changes outside the parenthesis of the function.Memory TipOutside the input values
  28. Card 28
    HintInput x is doubled.Memory TipHorizontal compression x by a factor of 2

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