Question 1Easier
A linear function is defined by . If , what is the value of ?
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Answer: C — 7
Substitution gives . Adding 8 and then dividing by 3 gives .
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Linear functions — SAT practice questions
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What this topic is
Linear functions are written in function notation, such as f(x) = mx + b, where m is the constant rate of change and b is the output when the input is zero.
Questions ask for an input that produces a given output, for an output from a slope and one known point, or for the meaning of a coefficient in context. A frequent mix-up is finding f(x) when the question asks for x, or the reverse.
Modeling questions describe temperature, cost or distance changing at a steady rate, and units matter: if the input counts hundreds of meters, the final answer may need converting to meters.
Sample questions
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Question 2Mid
The linear function has slope , and . What is the value of ?
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Answer: B —
The input increases by 5 from to 4, so the output changes by . Therefore, .
Question 3Mid
The function models the air temperature, in degrees Celsius, at a height of hundreds of meters above a reference elevation. At what height, in meters, does the model predict an air temperature of 13.8 degrees Celsius?
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Answer: C — 1,200
Solving gives . Since is measured in hundreds of meters, the height is meters.
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More SAT topics
Math
- Linear equations in one variable
- Linear equations in two variables
- Systems of two linear equations in two variables
- Linear inequalities in one or two variables
- Equivalent expressions
- Nonlinear equations and systems
- Nonlinear functions
- Ratios, rates, proportional relationships, and units
- Percentages
- One-variable data: distributions and measures
- Two-variable data: models and scatterplots
- Probability and conditional probability
- Inference from sample statistics and margin of error
- Evaluating statistical claims
- Area and volume
- Lines, angles, and triangles
- Right triangles and trigonometry
- Circles
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