Guided Practice
Overview
This lesson provides structured practice with functions. Work through problems involving function notation, evaluating functions, and identifying linear vs. non-linear functions.
Practice Problems
Question 1: If f(x) = 3x - 5, find f(4).
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Answer: 7
f(4) = 3(4) - 5 = 12 - 5 = 7
Question 2: Is the relation {(1,2), (2,4), (3,6), (1,8)} a function? Why or why not?
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Answer: No, it is not a function.
The input 1 maps to both 2 and 8. In a function, each input can only have one output.
Question 3: If g(x) = x² + 2x, find g(-3).
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Answer: 3
g(-3) = (-3)² + 2(-3) = 9 - 6 = 3
Question 4: A function f(x) = 2x + b passes through the point (3, 11). Find b.
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Answer: b = 5
11 = 2(3) + b, so 11 = 6 + b, b = 5
Question 5: Given f(x) = 4x - 1, find x when f(x) = 15.
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Answer: x = 4
15 = 4x - 1, so 16 = 4x, x = 4
Question 6: Is y = 3x² a linear function?
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Answer: No
Linear functions have the form y = mx + b. The x² term makes this a quadratic (non-linear) function.
Question 7: If h(x) = -2x + 7, find h(0) + h(1).
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Answer: 12
h(0) = -2(0) + 7 = 7. h(1) = -2(1) + 7 = 5. Sum = 7 + 5 = 12
Question 8: Find the slope and y-intercept of f(x) = -3x + 8.
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Answer: Slope = -3, y-intercept = 8
In f(x) = mx + b form, m = -3 is the slope and b = 8 is the y-intercept.
Question 9: If f(x) = x + 5 and g(x) = 2x, find f(g(3)).
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Answer: 11
First find g(3) = 2(3) = 6. Then f(6) = 6 + 5 = 11
Question 10: The table shows x: 1,2,3,4 and y: 5,8,11,14. Is this a linear function? If so, write the equation.
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Answer: Yes, f(x) = 3x + 2
The rate of change is constant: 8-5=3, 11-8=3, 14-11=3. Slope = 3. Using (1,5): 5 = 3(1) + b, b = 2.