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Can you draw different functions that have the same x-intercepts and the same domain and range?

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User Parmeet
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I'm pretty sure the answer is no. A function looks like this: f(x) = mx + c. Let's add another function, f(y) = ny + d. If the x-intercept is the same, we can subtract c and d from their respective equations. f(x) = mx, f(y) = ny. If the domains are the same, then x and y can have the same value, so we divide it out. f(x) = m, f(y) = n. Finally, if the ranges are the same, the value of f(x) = f(y). So by the substitution property, m=n. Since all the variables equal each other, both functions are equal to f(x) = mx+c! Therefore, they can only be the same function.

Answer: No
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User Deramko
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