Questions and Answers
Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) − 3?
Given the function f(x) = −2x² + 3x + 10, find f(1) and f(3). Choose the statement that is true concerning these two values.
Which equation best compares the slopes of the two functions?
Choose the equation that represents the line passing through the point (−3, −1) with a slope of 4.
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If f(x) is the height, in cm, of a sunflower plant that is x days old, what does f(60) = 210 mean?
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Choose the equation that represents the graph of a line passing through points (-3, 0) and (0, 3).
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Find and interpret the meaning of the x‐intercept in this scenario: Distance from school as a function of time.
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Which of the following describes the intercepts on the graph showing the velocity f(t) of a runner?
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What is the value of k for the graphs of f(x) and g(x) = f(x) + k?
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Choose the ordered pair that represents a possible domain and range of the function f(x), where f(x) is the number of parts produced per hour.
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Determine the equation of the line shown in the graph of a vertical line with an x-intercept of 5.
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Which of the following best describes the steps to draw the graph of a telephone company's charges?
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Which of the following does not represent a function?
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Compare the y-intercepts and slopes of the linear functions f(x) and g(x).
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Write an equation in function form to show the number of cars seen each week by the mechanic, given the context of a car manufacturer's recall.
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Study Notes
Linear Functions Overview
- Replacing f(x) with f(x) - 3 results in a vertical shift of the graph down by 3 units.
Function Evaluation
- For f(x) = -2x² + 3x + 10, f(1) > f(3), indicating f(1) is a greater value than f(3).
Function Comparison
- Function A: f(x) = 6x - 1 has a slope that is twice the slope of Function B.
Slope and Point Identification
- The equation of the line through (-3, -1) with a slope of 4 is y = 4x + 11.
Function Interpretation
- f(60) = 210 means that a sunflower plant reaches a height of 210 cm at 60 days old.
Line Equation Derivation
- The line passing through (-3, 0) and (0, 3) can be expressed as y = x + 3.
X-Intercept Meaning
- In the distance function table, the x-intercept (27, 0) represents the time taken to reach the school.
Velocity Function Analysis
- The initial velocity of a runner is 4 m/s, stopping after 8 seconds, as shown by the velocity graph.
Shift in Functions
- For functions f(x) and g(x) = f(x) + k, the constant k is -2, representing a vertical shift of the graph.
Domain and Range Representation
- An ordered pair (5, 10) illustrates a potential domain (input) and range (output) for a factory's production function.
Vertical Line Representation
- A vertical line with an x-intercept at 5 is represented by the equation x = 5.
Graphing Relationships
- A telephone company's charges can be graphed by connecting points (155, 100) and (245, 200), with a slope of 0.9.
Function Identification
- A parabola symmetric about the x-axis, with an x-intercept at -5, does not meet the criteria for being a function.
Comparison of Linear Functions
- In comparing linear functions f(x) and g(x), f(x) has a lesser slope but equal y-intercepts to g(x).
Linear Equation for Car Repairs
- The car manufacturer’s weekly repair function is linear, represented as f(x) = -5x + 250 after addressing a reduction in repairs over weeks.
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Description
This quiz covers key concepts related to linear functions, including function evaluation, comparison, and interpretation. Analyze slopes, shifts, and derive line equations while understanding their application in various contexts.
