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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?
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?
How does a vertical reflection affect the graph of the function 𝑓?
How does a vertical reflection affect the graph of the function 𝑓?
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?
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Which transformation describes a vertical reflection followed by a vertical shift upwards?
Which transformation describes a vertical reflection followed by a vertical shift upwards?
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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 $f(x)$?
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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 $g(x) = -f(x)$?
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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 $g(x) = f(x - 2)$?
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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?
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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 $g(x)$?
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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 $g(x) = -f(x + 5) + 2$?
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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 $f(x)$?
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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 $g(x)$?
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What is the expression for 𝑔(𝑥) if 𝑓(𝑥) = 4𝑥 + 3?
What is the expression for 𝑔(𝑥) if 𝑓(𝑥) = 4𝑥 + 3?
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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?
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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]?
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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)?
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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)?
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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?
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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)?
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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]?
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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.
