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Transformations of Cubic & Quartic Functions

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Wize High School Grade 12 Pre-Calculus Textbook > Polynomial Functions

Transformations of Cubic & Quartic Functions

7 Activities

Wize High School Algebra II Textbook (Common Core) > Polynomial Functions

Transformations of Cubic & Quartic Functions

7 Activities

Practice: Transformations of Cubic & Quartic Functions

The function f(x)=−32(47(x+2))4+1f(x)=-\dfrac{3}{2}\Bigg(\dfrac{4}{7}(x+2)\Bigg)^4+1 has been transformed from its parent function f(x)=x4f(x)=x^4.

Choose the correct transformations that have been applied to f(x)f(x) and choose the correct order:
  1. A vertical reflection about the x-axis
  2. A horizontal reflection about the y-axis
  3. A horizontal translation 2 units left
  4. A horizontal translation 2 units right
  5. A vertical translation 1 unit up
  6. A vertical translation 1 unit down
  7. A vertical compression by a factor of 23\dfrac{2}{3}
  8. A vertical expansion by a factor of 32\dfrac{3}{2}
  9. A horizontal compression by a factor of 47\dfrac{4}{7}
  10. A horizontal expansion by a factor of 74\dfrac{7}{4}


More Transformations of Cubic & Quartic Functions Questions:
Transformations of Cubic & Quartic Functions
Practice: Transformations of Cubic & Quartic Functions
The function f(x)=x3f(x)=x^3 has undergone the following transformations:
Horizontal‾Vertical‾Reflection about the x-axisExpansion by a factor of 107Compression by a factor of 56Translation 0.5 units rightTranslation 4 unit up\begin{array}{l cc l} \underline{\text{Horizontal}}&&&\underline{\text{Vertical}}\\\\ &&&\text{Reflection about the x-axis}\\\\ \text{Expansion by a factor of}~\frac{10}{7}&&&\text{Compression by a factor of}~\frac{5}{6}\\\\ \text{Translation 0.5 units right}&&&\text{Translation 4 unit up} \end{array}
Transformations of Cubic & Quartic Functions
Practice: Transformations of Cubic & Quartic Functions
The function f(x)=x4f(x)=x^4 has undergone the following transformations:
Horizontal‾Vertical‾Reflection about the y-axisReflection about the x-axisCompression by a factor of 23Expansion by a factor of 54Translation 2 units rightTranslation 4 units down\begin{array}{l cc l} \underline{\text{Horizontal}}&&&\underline{\text{Vertical}}\\\\ \text{Reflection about the y-axis}&&&\text{Reflection about the x-axis}\\\\ \text{Compression by a factor of}~\frac{2}{3}&&&\text{Expansion by a factor of}~\frac{5}{4}\\\\ \text{Translation 2 units right}&&&\text{Translation 4 units down} \end{array}
Transformations of Cubic & Quartic Functions
Practice: Transformations of Cubic & Quartic Functions
Graph the function f(x)=12(x−3)4−1f(x)=\frac{1}{2}(x-3)^4-1.
Transformations of Cubic & Quartic Functions
Practice: Transformations of Cubic & Quartic Functions
Graph the function f(x)=−(−x−3)3−5f(x)=-(-x-3)^3-5.
Transformations of Cubic & Quartic Functions
Practice: Transformations of Cubic & Quartic Functions
The function f(x)=−49(49(5−x))2+4f(x)=-\frac{4}{9}(\frac{4}{9}(5-x))^2+4 has been transformed from its parent function f(x)=x2f(x)=x^2.
Choose the correct transformations that have been applied to f(x)f(x) and choose the correct order:
More Transformations of Cubic & Quartic Functions Questions:
Transformations of Cubic & Quartic Functions
Practice: Transformations of Cubic & Quartic Functions
The function f(x)=x3f(x)=x^3 has undergone the following transformations:
Horizontal‾Vertical‾Reflection about the x-axisExpansion by a factor of 107Compression by a factor of 56Translation 0.5 units rightTranslation 4 unit up\begin{array}{l cc l} \underline{\text{Horizontal}}&&&\underline{\text{Vertical}}\\\\ &&&\text{Reflection about the x-axis}\\\\ \text{Expansion by a factor of}~\frac{10}{7}&&&\text{Compression by a factor of}~\frac{5}{6}\\\\ \text{Translation 0.5 units right}&&&\text{Translation 4 unit up} \end{array}
Transformations of Cubic & Quartic Functions
Practice: Transformations of Cubic & Quartic Functions
The function f(x)=x4f(x)=x^4 has undergone the following transformations:
Horizontal‾Vertical‾Reflection about the y-axisReflection about the x-axisCompression by a factor of 23Expansion by a factor of 54Translation 2 units rightTranslation 4 units down\begin{array}{l cc l} \underline{\text{Horizontal}}&&&\underline{\text{Vertical}}\\\\ \text{Reflection about the y-axis}&&&\text{Reflection about the x-axis}\\\\ \text{Compression by a factor of}~\frac{2}{3}&&&\text{Expansion by a factor of}~\frac{5}{4}\\\\ \text{Translation 2 units right}&&&\text{Translation 4 units down} \end{array}
Transformations of Cubic & Quartic Functions
Practice: Transformations of Cubic & Quartic Functions
Graph the function f(x)=12(x−3)4−1f(x)=\frac{1}{2}(x-3)^4-1.
Transformations of Cubic & Quartic Functions
Practice: Transformations of Cubic & Quartic Functions
Graph the function f(x)=−(−x−3)3−5f(x)=-(-x-3)^3-5.
Transformations of Cubic & Quartic Functions
Practice: Transformations of Cubic & Quartic Functions
The function f(x)=−49(49(5−x))2+4f(x)=-\frac{4}{9}(\frac{4}{9}(5-x))^2+4 has been transformed from its parent function f(x)=x2f(x)=x^2.
Choose the correct transformations that have been applied to f(x)f(x) and choose the correct order: