
Transformations of Linear Functions
Flashcard
•
Mathematics
•
6th - 8th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a linear function?
Back
A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.
2.
FLASHCARD QUESTION
Front
What does the slope of a linear function represent?
Back
The slope (m) of a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).
3.
FLASHCARD QUESTION
Front
What is the y-intercept of a linear function?
Back
The y-intercept (b) of a linear function is the point where the graph of the function crosses the y-axis. It represents the value of f(x) when x = 0.
4.
FLASHCARD QUESTION
Front
How does the graph of g(x) = f(x) + c differ from f(x)?
Back
The graph of g(x) = f(x) + c is a vertical shift of the graph of f(x) by c units. If c is positive, the graph shifts up; if c is negative, it shifts down.
5.
FLASHCARD QUESTION
Front
What effect does multiplying a function by a constant have on its graph?
Back
Multiplying a function by a constant (g(x) = kf(x)) stretches or compresses the graph vertically. If k > 1, the graph stretches; if 0 < k < 1, it compresses.
6.
FLASHCARD QUESTION
Front
What is the transformation represented by g(x) = f(x) - 4?
Back
The transformation g(x) = f(x) - 4 represents a vertical shift of the graph of f(x) downwards by 4 units.
7.
FLASHCARD QUESTION
Front
What does g(x) = 3f(x) indicate about the graph of f(x)?
Back
The equation g(x) = 3f(x) indicates that the graph of f(x) is stretched vertically by a factor of 3.
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