Which two equations represent the same function?
A) y = 2x – 7 and f(x) = 7 – 2x
<span>B) 3x = y – 2 and f(x) = 3x – 2</span>
<span>C) f(x) = 3x2 + 5 and y = 3x2 + 5</span>
D) None of the above
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<span>A) <span>y </span>= 2x – 7 and f(x) = 7 – 2x</span>
Incorrect. <span>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.</span>
B) 3x = y – 2 and f(x) = 3x – 2
Incorrect. <span>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 <span>y </span>= 3<span>x + </span>2. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5.</span>
C) f(x) = 3x2 + 5 and y = 3x2 + 5
Correct. <span>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. </span>D) None of the above
Incorrect. <span>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.
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