Which two equations represent the same function?
A) y = 2x – 7 and f(x) = 7 – 2x
B) 3x = y – 2 and f(x) = 3x – 2
C) f(x) = 3x2 + 5 and y = 3x2 + 5
D) None of the above
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A) y = 2x – 7 and f(x) = 7 – 2x
Incorrect. These equations look similar but are not the same. The first has a slope of 2 and a y-intercept of −7. The second function has a slope of −2 and a y-intercept of 7. It slopes in the opposite direction. They do not produce the same graph, so they are not the same function. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5.
B) 3x = y – 2 and f(x) = 3x – 2
Incorrect. These equations represent two different functions. If you rewrite the first equation in terms of y, you’ll find the equation of the function is y = 3x + 2. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5.
C) f(x) = 3x2 + 5 and y = 3x2 + 5
Correct. The expressions that follow f(x) = and y = are the same, so these are two different ways to write the same function: f(x) = 3x2 + 5 and y = 3x2 + 5. D) None of the above
Incorrect. Look at the expressions that follow f(x) = and y =. If the expressions are the same, then the equations represent the same exact function. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5.
