Polynomial Functions and Equations — Test

Question 12 • Mathematics III

Which graph can be used to find the solution(s) to 4 x is equal to negative 4 x ?

Answer

Image with description On a coordinate plane, the x and y axes ranges from negative 6 to 6 with an increment of 1 unit. One of the lines passes through point 4 comma 0 and 0 comma negative 4. The other line passes through point 0 comma 4 and negative 4 comma 0.

Image with description On a coordinate plane, the x and y axes ranges from negative 6 to 6 with an increment of 1 unit. There are two lines and both the lines are parallel to x-axis. One passes through point 0 comma negative 4 and the other line goes through point 0 comma 4.

Image with description On a coordinate plane, the x and y axes ranges from negative 6 to 6 with an increment of 1 unit. One of the lines passes through 4 comma 0 and 2 comma 2. The other line passes through negative 4 comma 0 and negative 2 comma 2.

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 6 to 6 with an interval of 1 unit. One of the lines passes through (1 comma 4) and (negative 1 comma negative 4). The other line goes through (1 comma negative 4) and (negative 1 comma 4).

Explanation

To solve 4x = −4x by graphing, graph the two sides as y = 4x and y = −4x. The first line passes through (1, 4) and (−1, −4), while the second passes through (1, −4) and (−1, 4), matching choice D. They intersect at (0, 0), so the solution is x = 0.

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