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Questions and Answers
What is the value of b in the equation y = -4/3x + 14?
What is the value of b in the equation y = -4/3x + 14?
-4/3
Which of the following transformations result in the equation y = -f(x)? (Select all that apply)
Which of the following transformations result in the equation y = -f(x)? (Select all that apply)
- Vertical stretch by a factor of 2
- Reflection in the x-axis (correct)
- Reciprocal transformation (correct)
- None of the above
What is the domain and range of the function f(x) = x^2 - 1?
What is the domain and range of the function f(x) = x^2 - 1?
- Domain: x ≥ -1, Range: y ∈ R
- Domain: x ∈ R, Range: y ≥ -1 (correct)
- Domain: x ∈ R, x ≠ ±1 Range: y ∈ R, y ≠ 0
- Domain: x ∈ R, Range: y ≥ -2
Draw the graph of y = f(-2x), what is the largest x-intercept?
Draw the graph of y = f(-2x), what is the largest x-intercept?
The inverse graph is always a function.
The inverse graph is always a function.
The graph of the inverse function is reflected along the line y = __.
The graph of the inverse function is reflected along the line y = __.
What is the new point after applying the transformation y = f(2x + 4) to the point (8, -5)?
What is the new point after applying the transformation y = f(2x + 4) to the point (8, -5)?
What happens when a reciprocal graph has a y-value of ±1?
What happens when a reciprocal graph has a y-value of ±1?
What is the result of the transformation f(x + 1) - 2?
What is the result of the transformation f(x + 1) - 2?
Match the transformation with the correct description:
Match the transformation with the correct description:
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Study Notes
Transformations Practice Exam - ANSWERS
Domain and Range
- The graph of f(x) = x^2 - 1 is a parabola with domain x ∈ R and range y ≥ -1.
Graph Transformations
- The graph of y = f(-2x) is obtained by multiplying x-values by 2 and reflecting across the y-axis.
- The graph of y = f(x - 2) + 4 is obtained by moving the original graph right 2 units and up 4 units.
Invariant Points
- Invariant points on the graph of a reciprocal occur when the original has a y-value equal to 1 or -1.
- The invariant points on the graph of a reciprocal occur four times, at the points indicated.
Graph of the Inverse
- The graph of the inverse is reflected in the line y = x.
- The inverse graph does not pass the vertical line test, therefore it is not a function.
Stretching and Reflections
- The graph of y = f(x/2) is obtained by applying a horizontal stretch by a factor of 2 to the original graph.
- The graph of y = -2f(x) is obtained by applying a vertical stretch by a factor of 2 and reflecting in the x-axis.
Translations
- The graph of y = f(x + 1) - 2 is obtained by applying a horizontal shift of 1 unit left and a vertical shift of 2 units down.
- The graph of y = f(2x) is obtained by applying a horizontal compression by a factor of 2.
Compositions of Transformations
- The graph of y = -f(-x) is obtained by reflecting in the y-axis and then in the x-axis.
- The graph of y = f(2x + 4) is obtained by applying a horizontal shift of 2 units left, a horizontal compression by a factor of 2, and a vertical shift of 4 units up.
Quadrantal Invariance
- In quadrant II, a reflection in the y-axis occurs.
- In quadrant III, a reflection in both axes occurs.
- In quadrant IV, a reflection in the x-axis occurs.
Inverse Graphs
- The graph of the inverse is reflected in the line y = x.
- Invariant points in the graph of the inverse occur when y = ±1.
Vertical Asymptotes
- Vertical asymptotes in the graph of a reciprocal occur at the x-intercepts of the original graph.
Stretching and Reflections
- The graph of y = 3f(x) is obtained by applying a vertical stretch by a factor of 3.
- The graph of y = -f(x) is obtained by reflecting in the x-axis.
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