Which equation defines the function f?

Question

The table below gives several values of x and their corresponding values of f(x) for the linear function f.

x    | f(x)
0    | 7
1    | 10
2    | 13
3    | 16

Accepted Answer

C. f(x) = 3x + 7. Each time x increases by 1, f(x) increases by 3, so the slope is 3; when x = 0, f(x) = 7, so the y-intercept is 7. Thus f(x) = 3x + 7, which checks for every row (e.g., f(2) = 3(2) + 7 = 13). Choice A uses the correct intercept but a slope of 1, ignoring that outputs rise by 3 per step. Choice B swaps the slope and the intercept. Choice D uses the correct slope but takes the intercept from the x = 1 row instead of the x = 0 row.

Answer

A. f(x) = x + 7 — You used the correct y-intercept of 7, but a slope of 1; the outputs go up by 3 for each increase of 1 in x, so the slope is 3.

Answer

B. f(x) = 7x + 3 — You swapped the slope and the intercept — the rate of change is 3 and the value at x = 0 is 7, so it's 3x + 7, not 7x + 3.

Answer

D. f(x) = 3x + 10 — Your slope of 3 is right, but you took the intercept from the x = 1 row; the y-intercept is the output when x = 0, which is 7.

Algebra practice question

Answer: C. f(x) = 3x + 7

Why the other answers are wrong

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