AlgebraVery hardComparing rates of two linear functions
Algebra practice question
Function f is defined by f(x) = 4x − 3. Function g is linear, with g(0) = 5 and g(2) = 9. Which statement is true?
- A. f increases faster than g, and f(x) > g(x) for all x > 4.Correct
- B. g increases faster than f.
- C. f and g increase at the same rate.
- D. f(x) > g(x) for all x > 0.
Answer: A. f increases faster than g, and f(x) > g(x) for all x > 4.
g has slope (9 − 5)/2 = 2 and intercept 5: g(x) = 2x + 5. f's slope 4 is greater. f(x) > g(x) when 4x − 3 > 2x + 5, i.e. x > 4.
Why the other answers are wrong
- B. g increases faster than f.
- g's slope is 2, less than f's 4.
- C. f and g increase at the same rate.
- The slopes are 4 and 2.
- D. f(x) > g(x) for all x > 0.
- At x = 1, f = 1 and g = 7; f overtakes g only after x = 4.
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