Podcast
Questions and Answers
Which transformation maps the graph of 𝑓 to the graph of 𝑔, defined by 𝑔(𝑥) = −𝑓(𝑥) + 5?
Which transformation maps the graph of 𝑓 to the graph of 𝑔, defined by 𝑔(𝑥) = −𝑓(𝑥) + 5?
- A vertical translation of the graph of 𝑓 by 5 units, followed by a vertical reflection.
- A vertical reflection of the graph of 𝑓, followed by a vertical translation. (correct)
- A horizontal translation of the graph of 𝑓 by 5 units, followed by a vertical reflection.
- A vertical reflection of the graph of 𝑓, followed by a horizontal translation.
What is the image of the graph of 𝑓, given by 𝑓(𝑥) = −𝑥^2 + 3𝑥 + 2, after a vertical translation by 4 units?
What is the image of the graph of 𝑓, given by 𝑓(𝑥) = −𝑥^2 + 3𝑥 + 2, after a vertical translation by 4 units?
- 𝑝(𝑥) = −𝑥² + 3𝑥 + 6. (correct)
- 𝑛(𝑥) = −(𝑥 − 4)² + 3(𝑥 − 4) + 2.
- 𝑞(𝑥) = −𝑥² + 3𝑥 − 2.
- 𝑚(𝑥) = −(𝑥 + 4)² + 3(𝑥 + 4) + 2.
How does a vertical reflection affect the graph of the function 𝑓?
How does a vertical reflection affect the graph of the function 𝑓?
- It reflects the graph across the y-axis.
- It translates the graph vertically downwards.
- It translates the graph vertically upwards.
- It reflects the graph across the x-axis. (correct)
What is the effect of performing a horizontal translation of the graph of 𝑓 by 5 units?
What is the effect of performing a horizontal translation of the graph of 𝑓 by 5 units?
Which transformation describes a vertical reflection followed by a vertical shift upwards?
Which transformation describes a vertical reflection followed by a vertical shift upwards?
How does the function $g(x) = f(x) + 4$ transform the graph of $f(x)$?
How does the function $g(x) = f(x) + 4$ transform the graph of $f(x)$?
What is the effect of the negative sign in the function $g(x) = -f(x)$?
What is the effect of the negative sign in the function $g(x) = -f(x)$?
If $f(x)$ has a domain of $[-4, 3]$, what would be the new domain for $g(x) = f(x - 2)$?
If $f(x)$ has a domain of $[-4, 3]$, what would be the new domain for $g(x) = f(x - 2)$?
For the transformation $g(x) = f(x + 4)$, where does the graph of $f(x)$ shift?
For the transformation $g(x) = f(x + 4)$, where does the graph of $f(x)$ shift?
If $f(x)$ is expressed as $f(x) = x^2 - 3x + 2$ and $g(x) = f(x) - 4$, what is $g(x)$?
If $f(x)$ is expressed as $f(x) = x^2 - 3x + 2$ and $g(x) = f(x) - 4$, what is $g(x)$?
What will be the range of $g(x)$ if $f(x)$ has a range of $(3, 9)$ and $g(x) = -f(x + 5) + 2$?
What will be the range of $g(x)$ if $f(x)$ has a range of $(3, 9)$ and $g(x) = -f(x + 5) + 2$?
When given $g(x) = f(x - 4) + 1$, how does this affect the original graph of $f(x)$?
When given $g(x) = f(x - 4) + 1$, how does this affect the original graph of $f(x)$?
In the context of $g(x) = f(x) + 2$, which is true regarding the graph of $g(x)$?
In the context of $g(x) = f(x) + 2$, which is true regarding the graph of $g(x)$?
What is the expression for 𝑔(𝑥) if 𝑓(𝑥) = 4𝑥 + 3?
What is the expression for 𝑔(𝑥) if 𝑓(𝑥) = 4𝑥 + 3?
If 𝑔(𝑥) = 𝑓(𝑥 - 2) + 5, what is 𝑔(4) given 𝑓(𝑥) = 2𝑥 - 5?
If 𝑔(𝑥) = 𝑓(𝑥 - 2) + 5, what is 𝑔(4) given 𝑓(𝑥) = 2𝑥 - 5?
What is the range of 𝑔(𝑥) = −𝑓(𝑥 + 3) + 1 if the range of 𝑓 is [−2, 4]?
What is the range of 𝑔(𝑥) = −𝑓(𝑥 + 3) + 1 if the range of 𝑓 is [−2, 4]?
For 𝑔(𝑥) = 𝑓(𝑥 + 5), what type of transformation occurs to the graph of 𝑓(𝑥)?
For 𝑔(𝑥) = 𝑓(𝑥 + 5), what type of transformation occurs to the graph of 𝑓(𝑥)?
If 𝑔(𝑥) = 𝑓(𝑥) + 2 and 𝑓(1) = 2, what is 𝑔(1)?
If 𝑔(𝑥) = 𝑓(𝑥) + 2 and 𝑓(1) = 2, what is 𝑔(1)?
What is the y-intercept of the function 𝑔(𝑥) = −𝑓(𝑥 + 3) + 2 if the y-intercept of 𝑓 is 3?
What is the y-intercept of the function 𝑔(𝑥) = −𝑓(𝑥 + 3) + 2 if the y-intercept of 𝑓 is 3?
Which equation represents a vertical shift downwards of 3 units of the function 𝑓(𝑥)?
Which equation represents a vertical shift downwards of 3 units of the function 𝑓(𝑥)?
What is the domain of the function 𝑔(𝑥) = 𝑓(𝑥 - 2) + 4 if the domain of 𝑓 is [−5, 3]?
What is the domain of the function 𝑔(𝑥) = 𝑓(𝑥 - 2) + 4 if the domain of 𝑓 is [−5, 3]?
Flashcards
Translation of a function (graphically)
Translation of a function (graphically)
Shifting the graph of a function horizontally or vertically.
Vertical translation (𝑓(𝑥) ± c)
Vertical translation (𝑓(𝑥) ± c)
Shifting the graph of 𝑓(𝑥) up or down by 'c' units.
Horizontal translation (𝑓(𝑥 ± c))
Horizontal translation (𝑓(𝑥 ± c))
Shifting the graph of 𝑓(𝑥) left or right by 'c' units.
Vertical Reflection ( −𝑓(𝑥) )
Vertical Reflection ( −𝑓(𝑥) )
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Combined transformations
Combined transformations
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Domain
Domain
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Range
Range
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Function Transformation
Function Transformation
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Vertical translation of a function
Vertical translation of a function
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Transformation of f(x) to g(x) in y=g(x)
Transformation of f(x) to g(x) in y=g(x)
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Vertical reflection of a function
Vertical reflection of a function
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Horizontal translation of a function
Horizontal translation of a function
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Function g(x) = -f(x) + 5
Function g(x) = -f(x) + 5
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𝑔(𝑥) = 𝑓(𝑥) + 𝑘
𝑔(𝑥) = 𝑓(𝑥) + 𝑘
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𝑔(𝑥) = 𝑓(𝑥 − ℎ)
𝑔(𝑥) = 𝑓(𝑥 − ℎ)
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𝑔(𝑥) = −𝑓(𝑥)
𝑔(𝑥) = −𝑓(𝑥)
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𝑔(𝑥) = 𝑓(−𝑥)
𝑔(𝑥) = 𝑓(−𝑥)
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Domain of a function
Domain of a function
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Range of a function
Range of a function
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Transforming Functions
Transforming Functions
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Numeric Transformation
Numeric Transformation
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Study Notes
Additive Transformations
- Additive transformations involve adding or subtracting a constant value to or from a function's output.
- These transformations shift the graph vertically.
- Adding a constant shifts the graph upward by that constant.
- Subtracting a constant shifts the graph downward by that constant.
Translations
- Transformations that shift the graph horizontally or vertically are called translations.
- Horizontal shifts involve adding or subtracting from the input variable.
- Adding a constant shifts the graph to the left by that constant.
- Subtracting a constant shifts the graph to the right by that constant.
Vertical Reflection
- A vertical reflection of a graph involves multiplying the function by -1.
- This reflects the graph across the x-axis.
Numerical Transformations
- Transformations using tables of values involve applying the transformation to the y-values.
- For example, f(x)+2 shifts the entire table by +2 in the vertical axis.
Domain and Range Transformations
- Transforming a function affects its domain and range.
- The domain and range of the transformed function g(x) are derived from the domain and range of the initial function f(x).
- Specific transformations can alter the domain and range by shifting bounds or reflecting across axes.
Algebraic Transformations
- Transformations applied directly to the function formula, such as g(x) = f(x) + 2.
- Expressions of g(x) in terms of x involve substituting the formula for f(x).
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Description
Test your understanding of additive transformations, translations, and vertical reflections in graph functions. This quiz covers how constant values affect the position of a graph on the coordinate plane. Get ready to explore numerical transformations and their impact on graphs.
